**Appendix**

 **B** **Table A1.** Included and Evaluated studies; Title, Author, Year, Journal, Summary, Topic, Evidence.

















*Sustainability* **2022**, *14*, 624


#### **Appendix C The Questionnaire**

#### **Introduction**

Civilian-Military Collaboration (CMC) is desired for the successful management of emergencies, disasters, and pandemics. This short survey aims to identify differences between two periods, BEFORE and DURING COVID-19 pandemic.

By conducting this survey, you agree to participate voluntarily. No name, affiliation, or other searchable information, but your profession and civilian/military status are registered. The data is handled in strict confidentiality and secure data storage and the study complies with the ethical principles stipulated by Swedish law, SFS 2008:192 and SFS 2003:460.

Please choose one of the options below, as indicated on the Likert Scale, for each question before and during the current COVID-19 pandemic in the table.

1: Weak 2: Fair 3: Undecided 4: Good 5: Strong

You may provide an example if needed. Comments are welcomed.

General information

A. Country: B. Gender: C. Profession: D. Civilian/Military E. Age: under 30 31–40 41–50 51–60 >60


#### **References**


## *Article* **A Critical Analysis of the COVID-19 Hospitalization Network in Countries with Limited Resources**

**Marcio L. V. Araujo 1,2,3,\*,†, José G. V. Miranda 4,†, Rodrigo N. Vasconcelos 5,†, Elaine C. B. Cambui 6,†, Raphael S. Rosário 4,†, Márcio C. F. Macedo 4,†, Antonio C. Bandeira 7,†, Márcia S. P. L. Souza 7,†, Ana C. F. N. Silva 7,†, Aloisio S. Nascimento Filho 3,8,†, Thiago B. Murari 3,8,†, Eduardo M. F. Jorge 3,9,† and Hugo Saba 1,3,9,†**


**Abstract:** To effectively combat the COVID-19 pandemic, countries with limited resources could only allocate intensive and non-intensive care units to a low number of regions. In this work, we evaluated the actual displacement of infected patients in search of care, aiming to understand how the networks of planned and actual hospitalizations take place. To assess the flow of hospitalizations outside the place of residence, we used the concepts of complex networks. Our findings indicate that the current distribution of health facilities in Bahia, Brazil, is not sufficient to effectively reduce the distances traveled by patients with COVID-19 who require hospitalization. We believe that unnecessary trips to distant hospitals can put both the sick and the healthy involved in the transport process at risk, further delaying the stabilization of the COVID-19 pandemic in each region of the state of Bahia. From the results found, we concluded that, to mitigate this situation, the implementation of health units in countries with limited resources should be based on scientific methods, and international collaborations should be established.

**Keywords:** government; hospitalization; pandemics; public policy; transportation

#### **1. Introduction**

The state of Bahia, Brazil, has a total area of approximately 565,000 square kilometers and, by the end of 2020, had an estimated population of about 15 million people, which

**Citation:** Araujo, M.L.V.; Miranda, J.G.V.; Vasconcelos, R.N.; Cambui, E.C.B.; Rosário, R.S.; Macedo, M.C.F.; Bandeira, A.C.; Souza, M.S.P.L.; Silva, A.C.F.N.; Nascimento Filho, A.S.; et al. A Critical Analysis of the COVID-19 Hospitalization Network in Countries with Limited Resources. *IJERPH* **2022**, *19*, 3872. https:// doi.org/10.3390 ijerph19073872

Academic Editors: Amir Khorram-Manesh and Krzysztof Goniewicz

Received: 8 February 2022 Accepted: 21 March 2022 Published: 24 March 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

is superior to the estimated population of European countries, such as Belgium, Greece, Sweden, and Portugal [1]. The human development index (HDI) of the state of Bahia is 0.660, similar to other countries with limited resources such as Guatemala, Honduras, India, Bangladesh, and Morocco. In this sense, while in normal conditions it is already difficult to provide free, high-quality health care services to the population that live in Bahia, on 11 March 2020, with the World Health Organization (WHO) announcement of the coronavirus disease 2019 (COVID-19) outbreak, caused by the new severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), as a pandemic, the provision of high-quality health care services has become even more challenging, since the high transmissibility of SARS-CoV-2 may quickly overload the health care services of a state or a country [2].

Possibly inspired by the National Health Service of the United Kingdom [3], the Brazilian National Health System (Sistema Único de Saúde—SUS) is a public health system created by the Constitution of the Federative Republic of Brazil [4]. The SUS is a universal access system, which allows any Brazilian to use low-, medium-, and high-complexity health services. In addition, management is divided between federal, state, and municipal sectors. States and municipalities have autonomy in defining policies in favor of health [5]. Previous studies in Brazil have found that, although there was a favorable expansion in Universal Health Coverage (UHC), structural problems remained in the SUS, from gaps in organization and governance to a scarcity of public resources. Thus, it is evident that there are regional disparities in terms of health services [6]. However, the geographic and economic differences do not allow for a comparison between these countries in terms of the flow of hospitalization. Previous works deal with the use of resources in health services [7,8]. This work aims to analyze the flow of hospitalizations in a country with limited resources. The displacement of patients receiving hospital treatment during the COVID-19 pandemic has proved to be a problem for some countries [9,10].

In the state of Bahia, Brazil, the management of SUS is done by the state government of Bahia, which must provide financial resources and stimulate the municipalities of Bahia to achieve the responsible management of their health care services, and must also assume that responsibility in the case some of those municipalities are not able to achieve that goal [5]. As resources are limited and the territorial space of Bahia is large, the creation of health units, in a few areas, is presented as a single alternative, so large displacements of infected patients are inevitable.

By the end of October 2020, following the State Contingency Plan for Confrontation of the New Coronavirus SARS-CoV-2 [11], the state government of Bahia distributed 2286 intensive and non-intensive care units in 61 out of the 417 municipalities of Bahia, in order to provide better assistance to the COVID-19 patients that live in Bahia [12], 41% higher than the previous healthcare network. In Bahia, the room availability follows a protocol based on clinical severity, risk potential, health problems or degree of suffering [13]. Many of these health rooms were created to serve COVID-19 patients, as part of a municipal, state, and federal effort. Therefore, COVID-19 patients that reside in municipalities not capable of providing appropriate treatment or hospitalization for such a disease must travel to another municipality to be better assisted by SUS. In order to reduce the distance and duration of those travels, the state government of Bahia has distributed health care units into municipalities located into nine regions (i.e., North, Northeast, North-Central, East-Central, East, West, Southwest, South, and Extreme-South) that geographically divide the state of Bahia, such that COVID-19 patients could be ideally treated or hospitalized in health care units available at the regions where they reside, promoting a region-based control of the COVID-19 pandemic inside the state of Bahia.

Related work has already shown that we need to analyze transportation networks between the municipalities and states of a country [14–17] to be able to study the dynamics of dissemination of infectious diseases, such as COVID-19 [18–24], as well as to evaluate how we can guarantee a safe transportation for COVID-19 patients to be hospitalized in the health care units [25–27] of Bahia.

In this paper, we aim to evaluate whether the distribution of intensive and nonintensive care units among 61 out of the 417 municipalities in Bahia is sufficient to assist COVID-19 patients inside each one of the nine distinct regions that divide the state of Bahia. On the basis of a dataset provided by the Health Secretary of the State of Bahia (Secretária de Saúde do Estado da Bahia—SESAB) and by the Brazilian Ministry of Health (Ministério da Saúde do Brasil), from open health systems data, we have built a hospitalization network for COVID-19 patients in Bahia, Brazil, based on the concepts of complex networks and using geoprocessing. We have also analyzed whether COVID-19 patients are indeed being hospitalized in health care units located in the same region where they live, and if that is not the case, we determined the relation of importation and exportation of hospitalized COVID-19 patients between distinct regions in Bahia. The specificity of the study and the absence of an index that could be used to compare the level of care and hospitalization provided by a given region led to the development of the Degree of External Search for Hospitalization (DESH) index, used to estimate the saturation level of the municipalities that offer in-hospital assistance for COVID-19 patients that come from other regions of the state of Bahia.

The network approach allowed us to evaluate the relationship between the external demand for COVID-19 care units and the supply of these units in the region. The DESH measure does not represent a new topological index of the network, but rather a simple evaluation of the external pressure for care units in the municipality relativized with respect to the total number of care units available in it. We believe that the discussions presented in this paper may be helpful to the state government of Bahia, which may improve its decisionmaking process to effectively control the COVID-19 pandemic in Bahia, and we also believe that this kind of study may be replicated for other states and countries around the world to verify whether the hospitalization networks previously estimated by governments match the real ones obtained in practice.

#### **2. Materials and Methods**

#### *2.1. Data Collection*

In this study, we considered the COVID-19 patients that were hospitalized in intensive or non-intensive care units provided by SUS in the state of Bahia, Brazil, between 1 March 2020 and 30 July 2020, and that have been reported in the hospital systems. To build the hospitalization networks, the data represent all hospitalizations of patients affected by COVID-19 (4387) who were removed from their city of residence to another city. The objective was to measure the displacement of these patients due to the unavailability of health units in their municipality of residence.

#### *2.2. Hospitalization Network*

On the basis of the graph theory, we represent the hospitalization networks for COVID-19 patients in Bahia as a directed graph, where each node is assigned to a municipality in Bahia, each node's size is directly proportional to its DESH index to be presented in the next subsection, each directed edge represents a travel going from an origin (i.e., municipality of residence) to a destination (i.e., municipality of hospitalization), and each directed edge is weighted by the number of patients that traveled between the corresponding pair of origin–destination municipalities. Hence, the hospitalization networks provides a visual representation of the patients that needed to be hospitalized because of the severity of COVID-19, but could not be hospitalized in their municipality of residence due to the unavailability of a health care unit at that location and at that moment.

#### *2.3. Simulation of the Expected Network*

In order to evaluate whether the strategy of the state government of Bahia to distribute health care units among the nine regions in Bahia was successful, we simulated the expected hospitalization networks idealized by the state government. To do so, we redirected each edge of the observed hospitalization networks to connect the node representing the municipality of residence of the patient to another node representing the closest municipality with an available health care unit, such that each redirected edge could represent the expected path traveled by a patient when searching for hospitalization by COVID-19 in Bahia.

#### *2.4. DESH (Degree of External Search for Hospitalization) Index*

To favor a comparison between the level of assistance and hospitalization provided by each region of the state of Bahia, we have developed the DESH index. With such an index, we can measure the saturation level of the 61 municipalities able to hospitalize COVID-19 patients. While each one of those 61 municipalities must provide assistance to the internal demand for hospitalization, by providing support to the patients that live inside the corresponding municipality, the DESH index only takes into account the external demand for hospitalization. In other words, this index measures how much each municipality is involved in the importation of COVID-19 patients provided by other municipalities that could be located inside or outside of the corresponding region of the state of Bahia.

The DESH index of a municipality i, or node i, with at least one intensive or nonintensive care unit available can be described in terms of Equation (1):

$$DESH\_i = \frac{\sum\_{j=1}^{N-1} w\_{ij}}{\gamma i} \tag{1}$$

where *wij* is the weight of a directed edge that connects node i to node *j* (i.e., the number of patients that traveled from municipality *j* to municipality *i*), *i* is the total number of intensive and non-intensive care units available at that municipality *i*, *N* is the total number of municipalities being evaluated, and *γ<sup>i</sup>* represents the municipalities.

Each one of the nine regions of Bahia is represented by a specific color. Each node (red circle) of the directed graph represents a municipality of Bahia. Each node size is directly proportional to its DESH index. The weight of each directed edge (black line) is directly proportional to the number of patients that have been transported to the corresponding municipality for hospitalization.

#### **3. Results**

As we can see in Figure 1a, according to the original planning of the state government of Bahia, even if not every one of the 417 municipalities of Bahia has a reference hospital or health care unit able to treat COVID-19 patients, the expected hospitalization networks for COVID-19 patients would be the one in which each patient would be hospitalized in the nearest reference unit available in the region where the patient is residing, such that COVID-19 patients would travel as minimum a distance as possible to be hospitalized, consequently allowing for a faster and more efficient treatment of those patients, as well as for a lower exposition to COVID-19 of the professionals involved in the transportation process. Hence, as can be seen by the weights of the directed edges shown in Figure 1a, once the health care units of each region would concentrate the hospitalization cases of the patients that live in the corresponding municipalities, the hospitalization networks would be more distributed all over the state, and the COVID-19 pandemic could be handled locally, per region of the state of Bahia. However, on the basis of the anonymized data collected from SESAB, we could estimate that the observed hospitalization networks for hospitalized patients are more similar to the one illustrated in Figure 1b. In this case, we can see that several COVID-19 patients need to travel from one region to another to be properly hospitalized, which suggests that some regions of the state of Bahia are not able to handle the high demands of hospitalization that may be happening due to COVID-19. In the ideal, expected scenario depicted in Figure 1a, each region would hospitalize only resident patients diagnosed with COVID-19. However, Table 1 shows that, while the North, East, and Southwest regions exported a few patients to the other regions of the state of Bahia, the North-Central, East-Central, and Northwest regions exported more than three times the number of patients that they could hospitalize. We also observed that both the East and Southwest regions concentrate the highest percentage of imported hospitalizations. In this case, it is worth noting that almost 50% of the hospitalizations done in the East region, which includes the capital of the state of Bahia, Salvador, are imported from other regions, while only 0.5% of the hospitalized cases are exported to other regions.

**Figure 1.** A visual comparison between the expected (**a**) and observed (**b**) hospitalization networks for COVID-19 patients in Bahia, Brazil. Source: Author.

**Table 1.** A numerical overview of the observed hospitalization networks for COVID-19 patients with respect to the nine regions of the state of Bahia.


#### **4. Discussion**

One of the main problems caused by such an unbalanced observed hospitalization networks is illustrated in Figure 2, which shows that, while in the expected hospitalization networks, some travel would be required to transport patients between the municipalities of the same region, in the observed scenario, more patients needed to travel longer distances to be hospitalized outside of their region of residence.

In our point of view, this unnecessary transportation of patients may affect the state of Bahia in two ways: First, this scenario may reduce the effectiveness in the reduction of the number of new cases of COVID-19 per region of the state of Bahia, since new patients diagnosed with COVID-19 might end up being hospitalized in another region that has already stabilized the COVID-19 pandemic, exposing the healthcare professionals of such a region to the coronavirus, which, once they are infected by COVID-19, could further disseminate the infectious disease to other people, contributing to a new rise in the number of new cases of COVID-19 per day. Second, this unnecessary transportation may result in additional costs for the state and the municipalities of Bahia, since they both are financially responsible for the management of the healthcare professionals and the infrastructure used to transport the patients to be hospitalized, and for the maintenance of the intensive and non-intensive care units that otherwise would be empty or at least less occupied, assuming a scenario in which a region is exporting new COVID-19 patients to be hospitalized to another region that has achieved stabilization with few new cases of COVID-19.

**Figure 2.** A histogram with the frequencies of expected (red) and observed (black) distances traveled by COVID-19 patients. Source: Author.

In Figures 3, 4, 5a, and 6, we show a more detailed visualization of the observed hospitalization networks previously shown in Figure 1b. These figures detail the transportation network for hospitalized COVID-19 patients with a focus on the relation between distinct regions of the state of Bahia and the East region, which contains the capital of the state of Bahia and the highest number of intensive and non-intensive care units, and concentrates the highest number of imported patients from other regions.

Many patients of the regions that are neighbours of the East region, such as the East-Central (Figure 3a), Northeast (Figure 5a), and South (Figure 6b) regions, are hospitalized in the East region, which may indicate that there is an unbalanced distribution of health care units in those neighbouring regions. Moreover, Figures 3, 4, 5a, and 6 show that the regions that are more distant to the East one, such as the North-Central (Figure 3b) and Extreme-South (Figure 4a) regions, also contribute to the exportation of patients to the East region. On the other hand, both the West (Figure 6a) and North (Figure 5b) regions are able to handle the demand for the hospitalization of their patients, even through the West region exported some patients for hospitalization to the East and Southwest regions, and the North region also exported some cases for hospitalization to the East region.

**Figure 3.** (**a**) A visualization of the East and East-Central regions. (**b**) A visualization of the East, East-Central, and North-Central regions. Source: Author.

**Figure 4.** (**a**) A visualization of the Extreme-South, East, South-West, and South regions. (**b**) A visualization of the East and South-West regions. Source: Author.

**Figure 5.** (**a**) A visualization of the East-Central, East, Northeast regions. (**b**) A visualization of the East and North regions. Source: Author.

**Figure 6.** (**a**) A visualization of the East, West, South-West regions. (**b**) A visualization of the East, South-West and South regions. Source: Author.

It is known that the state of Bahia has a health care regulation system, and it can be seen from the results of this research that the logistics included in the process of control and the distribution of care needs to be reviewed. This is not only based on the number of inhabitants per square meter in a health region or city, but also on the need for certain medical specialties and the growth in demand for care, suggesting that this may be the reality in other countries with limited resources.

#### **5. Conclusions**

As we have shown in this paper, the distribution of intensive and non-intensive care units in the state of Bahia, Brazil, is limited, since many patients had to travel more than 300 km to be hospitalized, as shown in Figure 2. Hence, a redistribution of the available health care units, or alternatively a selective, adaptive expansion of the health care infrastructure in the regions that are exporting most of their patients to be hospitalized in other regions, may contribute to a more successful reduction in the length of these travels.

COVID-19 is a dangerous infectious disease that requires new policies of the governments in order to effectively combat the further prolongation of this pandemic. Such policies could be based on scientific research that considers the local realities of the population and other variables that can provide optimized health facility distribution arrangements. In this sense, the provision and distribution of new hospitals and health care units based on scientific criteria that are capable of caring for and admitting patients with COVID-19 would allow for the faster and more effective treatment of these patients.

Finally, we hope that the publication of this manuscript will be an encouraging factor for the state government of Bahia, and other governments around the world, to reproduce the methodology presented in this paper, so as to better evaluate their care unit distribution policies. This approach allows for a clear visualization of demand pressure and migration between different regions, which can help to determine whether the expected strategies previously planned are being observed in practice and thus reducing the social and economic impact and, most importantly, saving lives.

**Author Contributions:** Conceptualization: M.L.V.A., J.G.V.M., R.N.V., E.C.B.C., M.S.P.L.S. and H.S.; methodology: all authors; software: M.L.V.A., J.G.V.M., R.N.V., E.C.B.C., R.S.R., E.M.F.J. and H.S.; validation: all authors; formal analysis: all authors; investigation: all authors; resources: M.L.V.A., A.C.B., M.S.P.L.S., A.C.F.N.S., A.S.N.F., T.B.M., E.M.F.J. and H.S.; data curation: M.L.V.A., J.G.V.M., M.S.P.L.S., A.C.F.N.S. and H.S.; writing—original draft preparation: all authors; writing—review and editing: all authors; visualization: all authors; supervision: M.L.V.A. and H.S.; project administration: M.L.V.A. and H.S.; funding acquisition: M.L.V.A., M.S.P.L.S., A.C.F.N.S. and H.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by PPSUS FAPESB: TO SUS0013/2021, grant number: 4370/2020. Received financial support from the National Council for Scientific and Technological Development— CNPq (http://cnpq.br/, accessed on 20 November 2021), grant numbers 306306/2021-2 (M.L.V.A.), 431990/2018-2 (H.S.) and 313423/2019-9 (H.S.).

**Institutional Review Board Statement:** Not applicable. The data used in this research were anonymous, without any personal data of the patients.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The original database used is public and available at https://bi.saude. ba.gov.br/transparencia/ (accessed on 22 October 2021), https://opendatasus.saude.gov.br/dataset/ srag-2020 (accessed on 22 October 2021), and https://opendatasus.saude.gov.br/dataset/srag-2021 -e-2022 (accessed on 22 October 2021). Summarized data from hospitalizations used in the analysis can be found at https://github.com/dataNPAI/UTIdata.git (accessed on 5 January 2022).

**Acknowledgments:** This work was supported by The Foundation for Research Support of the State of Bahia—FAPESB and the National Council for Scientific and Technological Development—CNPq.

**Conflicts of Interest:** The authors declare that there is no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

#### **Abbreviations**

The following abbreviations are used in this manuscript:


#### **References**


## *Review* **Health, Economic and Social Development Challenges of the COVID-19 Pandemic: Strategies for Multiple and Interconnected Issues**

**Sigamani Panneer 1,\*, Komali Kantamaneni 2,\*, Udhayakumar Palaniswamy 1, Lekha Bhat 1, Robert Ramesh Babu Pushparaj 1, Kesavan Rajasekharan Nayar 3, Hilaria Soundari Manuel 4, F. X. Lovelina Little Flower <sup>5</sup> and Louis Rice <sup>6</sup>**


**Abstract:** The COVID-19-pandemic-related economic and social crises are leading to huge challenges for all spheres of human life across the globe. Various challenges highlighted by this pandemic include, but are not limited to, the need for global health cooperation and security, better crisis management, coordinated funding in public health emergencies, and access to measures related to prevention, treatment and control. This systematic review explores health, economic and social development issues in a COVID-19 pandemic context and aftermath. Accordingly, a methodology that focuses on identifying relevant literature with a focus on meta-analysis is used. A protocol with inclusion and exclusion criteria was developed, with articles from 15 December 2019 to 15 March 2022 included in the study. This was followed by a review and data analysis. The research results reveal that non-pharmaceutical measures like social distancing, lockdown and quarantine have created long-term impacts on issues such as changes in production and consumption patterns, market crashes resulting in the closure of business operations, and the slowing down of the economy. COVID-19 has exposed huge health inequalities across most countries due to social stratification and unequal distribution of wealth and/or resources. People from lower socio-economic backgrounds lack access to essential healthcare services during this critical time for both COVID-19 and other non-COVID ailments. The review shows that there is minimal literature available with evidence and empirical backup; similarly, data/studies from all countries/regions are not available. We propose that there is a need to conduct empirical research employing a trans-disciplinary approach to develop the most effective and efficient strategies to combat the pandemic and its aftermath. There is a need to explore the social and ecological determinants of this contagious infection and develop strategies for the prevention and control of COVID-19 or similar infections in future.

**Keywords:** COVID-19; global economy; healthcare; social development; low- and middle-income countries; transdisciplinary research

#### **1. Introduction**

This paper explores the challenges of the COVID-19 pandemic and the significance of non-pharmaceutical measures for global health and socio-economic development. The

**Citation:** Panneer, S.; Kantamaneni, K.; Palaniswamy, U.; Bhat, L.; Pushparaj, R.R.B.; Nayar, K.R.; Soundari Manuel, H.; Flower, F.X.L.L.; Rice, L. Health, Economic and Social Development Challenges of the COVID-19 Pandemic: Strategies for Multiple and Interconnected Issues. *Healthcare* **2022**, *10*, 770. https://doi.org/ 10.3390/healthcare10050770

Academic Editor: Krzysztof Goniewicz

Received: 24 March 2022 Accepted: 17 April 2022 Published: 21 April 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

COVID-19 pandemic introduced economic and social crises that are posing huge challenges across the globe. The most serious challenges related to the COVID-19 pandemic and post-COVID future are related to the employment and incomes of millions of people, social security, income support schemes, the burden on women, the plight of migrants and informal sector workers, mental health issues, and restrictions on economic activity, including halted production, with firms unable to sell their goods and services [1]. The pandemic has also sparked fear and anxiety due to economic shocks and recession [2]. In an attempt to "flatten the curve", various countries' governments have imposed international border shutdowns [3,4], internal travel constraints [5] and longer periods of quarantine [6,7]. Economists have predicted that the COVID-19 pandemic will slow down Gross Domestic Product (GDP) growth by one-half a percentage point for 2020, and this applies to all countries (from 2.9% to 2.4%) [8]. Social distancing, lockdown and quarantine have high economic and social costs associated with them because they introduce changes in production and consumption patterns, which caused financial markets to crash, resulting in the closure of business operations [9]. Furthermore, this pandemic also introduced the international community to various challenges relating to global health cooperation and security, crisis management (investment in emergency preparedness) and coordinated funding during public health emergencies. The global economy has been very badly affected, especially the agro-livestock industry, hitting their lowest growth rates across various countries [10]. A decrease in inputs availability and a decrease in agricultural production during the pandemic affected food security as well [11].

Globally 3.3 billion people, which constitutes 81% of the world's workforce, were affected by the lockdown. Of this lockdown-affected workforce, 61% were workers from the informal sector, and of this 90% were from low- and middle-income countries [12,13]. The nationwide lockdowns during the COVID-19 pandemic disunited and isolated much of the migrant populations. Due to the lack of job opportunities, millions of migrant workers were forced to return to their countries/counties/villages in a time when public transportation was closed or severely restricted. Migrants faced humanitarian and health security challenges and unusual logistical nightmares from the states where they migrated [14]. Furthermore, in many developing and underdeveloped countries, the available social security measures are weak, with a lack of access to health care and economic security [15]. As many state borders were closed, inter-country travel and trade were shut and more than 30 million people fell into poverty in the absence of active policies to protect or substitute income flows to vulnerable populations. These policies, decisions and actions severely impacted the health and wellbeing of a large section of the population [16]. With chronic low funding in rural healthcare and the economy, the pandemic has revealed the weaknesses of rural infrastructure in almost all countries [17].

#### **2. Review Protocol**

A systematic review has been selected for this study with exclusion and inclusion criteria applied to narrow down the literature search. A large number of academic literature and policy documents related to COVID-19 have been considered for this study. Google, Google Scholar, PubMed, Science Direct, Web of Science and Scopus were used to identify the relevant literature. Google has been used to search various policy reports and other associated documents that are not available in scientific search engines such as Science Direct, Web of Science and Scopus. This review attempted to find solutions to health, economic and social development challenges of the COVID-19 pandemic. The major objectives of the review were to understand the inter-linkages between health, economy and society, to assess the pandemic crisis, to explore health and development implications of COVID-19, to compile possible and easily workable strategies for solving problems of COVID-19, to understand the role of multi-stakeholders in time of crisis and to document innovative collaborative strategic directions to control the pandemic. Based on these objectives, the search was made to look through each database that contained the terms: COVID-19, health and development challenges, pandemics, multiple and interconnected

issues, economic impact and strategies, prevention and recommendations. During the search, results from diverse sources identified some duplicate articles, especially those associated with COVID-19. Due to this, a unique combination of words was used to explore the relevant literature as follows:

COVID-19 and low- and middle-income countries COVID-19 and developed countries Stages of lockdown and health impacts Lockdown and economic impact COVID-19 and health impacts COVID-19—disaster management Post-pandemic context

Appropriate literature was identified from the diverse sources, based on data quality, focus area, rigourous methods, and removal of replicas; the subsequent works were scrutinised according to the exclusion and inclusion criteria listed in Table 1. This process was undertaken in different phases, with the date of publication, abstract and title considered for exclusion and inclusion. If the title and abstract did not fully reveal the scope of the study, the full article was examined to fully assess the entire information for that specific particular. Furthermore, some grey literature was considered for this study. Google and organization websites such as United Nations Development Programme (UNDP), World Health Organization (WHO), United Nations (UN), and United Nations Office for Outer Space Affairs (UNOOSA) were used to get the most up-to-date information. PICO was used as the strategy to undertake the systematic review.

**Table 1.** Criteria for the inclusion and exclusion.


Based on Google, Google Scholar, PubMed, Science Direct, Web of Science and Scopus, a total of 1825 relevant articles were identified. However, more than 600 (628) duplicates were identified and these were deleted. Moreover, literature that was not closely related to the search words led to the deletion of a further 426 articles. At this stage, 771 articles had been considered for assessment. After careful consideration of the titles and abstracts, a further 424 articles were removed. At this stage, 347 articles had been considered for the analysis. After reading these 347 papers, a further 202 articles were deleted, as they had either highly technical or overly sensitive issues. Finally, 145 papers were considered for the study. Of these 145 papers, Table 2 presents the top 10 papers, which are the most relevant

and highly cited articles. Figure 1 provides information on the inclusion and exclusion criteria of the literature.


**Figure 1.** Systematic review—PRISMA model flow diagram (inclusion and exclusion criteria).

#### **3. Review Results**

#### *3.1. Pandemics and Their Impact on Various Population Groups*

Pandemics/disasters often leave a significant impact on human health and development. This includes, but is not limited to, loss of human lives, livelihood issues, and psycho-social problems. Pandemics can create long-term imbalances in societies and communities. The challenges confronted by the general public due to the pandemic have revealed inadequacies in the areas of managing health risks, injuries, diseases, disabilities, psychological problems and deaths [18]. The COVID-19 pandemic has affected all aspects of human life and the global economy [19]. The World Trade Organization (WTO) and Organization for Economic Cooperation and Development (OECD) marked the COVID-19 pandemic as the greatest peril to the world economy since the financial emergency of 2008–2009 [20]. Emerging issues related to jobs and income of millions of people, social safety net, future of income support schemes, the burden on women, and the plight of migrants and informal sector workers are some of the main challenges that the world is confronting [21]. Oxfam predicts that the economic crisis due to COVID-19 could push half a billion people into poverty [22]. Due to the lockdown, economic activities and livelihoods were affected in many ways, especially in the fields such as production and distribution, consumption, restriction on trade and business, large-scale uncertainties in the market, lack of access to the resources and sudden disappearance of the more informal sectors of employment/sector [23]. The global outbreak has resulted in developmental impacts on health, education, gender, economy, politics and the environment. The COVID-19 pandemic has exposed huge health inequalities across countries and within countries due to existing social stratification and resource sharing. People from lower socio-economic

strata lack access to essential healthcare services during the pandemic time [24]. The economic decline during the pandemic has significantly affected people from the lower socio-economic stratum [23]. This pandemic has marked a significant impact on the lives of many vulnerable sections of society, including women and children. Across countries, the number of cases related to domestic violence has increased [25]. The pandemic has had an extensive impact on the education sector [26–28], and all educational institutions have been closed for several months, especially in countries where vaccination proceeded at a slower pace. The pandemic has forced a worldwide lockdown, with a huge number of citizens confined to their homes [29], often resulting in social isolation. Social isolation has led to chronic loneliness and boredom, which has affected mental health, human happiness and wellbeing [25].

The pandemic affected political systems across the globe, causing ideological differences, lack of need-based initiatives, geopolitical cooperation/dysfunctions, misinformation and misleading/false claims. The COVID-19 pandemic has affected religion in many ways, including cutting short pilgrimages and journeys related to religious practices and festivities [30]. People working in the informal sector, including migrant workers, are at a high risk of poverty as their income and livelihood options are limited [31,32]. Vulnerable populations have struggled to cope with the magnitude of problems and the incidence of suicide has increased due to loss of income, livelihood and other factors [33]. Challenges of immunization, nutrition, poverty, hunger, acute undernourishment, and health inequalities, especially amongst vulnerable groups, have posed severe health and economic challenges [31].

The pandemic's impact on social life, the economy and the financial sector has led millions of people to face an unprecedented situation related to poverty, wherein an average of 3.3 billion of the global workforce are at risk of losing their livelihoods [12,34]. Breadwinners working in the informal economy, particularly marginalized populations in low-income countries, which includes small-scale farmers and indigenous peoples, have been drastically affected [35]. According to a WHO survey, in May 2020, it was found that in 155 countries, the pandemic had severely curtailed people's ability to avail treatment services for Non-Communicable Diseases (NCDs). This situation is of significant concern because people living with non-communicable diseases tend to be at higher risk of severe COVID-19-related illness and death [36]. While the health systems of various countries are being challenged by the increasing demand for care of COVID-19 patients, it is imperative to maintain preventive and curative health care services, especially for the most vulnerable populations, such as children, women, older persons, people living with chronic conditions, minorities and people living with disabilities [37]. The pandemic has deepened pre-existing inequalities in social, political and economic systems, including access to health services and social protection. Women with care responsibilities, informal workers, low-income families and young people have been most adversely affected by the pandemic. There has also been a significant rise in domestic violence [38]. An increase in violence against women has resulted in a threat to public health and women's health across the globe. The health impacts of violence, particularly intimate partner or domestic violence, on women and children have significantly increased in various societies. Women who have been displaced, are refugees, and are living in conflict-affected areas are the most vulnerable [39]. Lack of education and economic insecurity has also increased the risk of gender-based violence. Without sufficient economic resources, women cannot escape from abusive partners and hence face a greater threat of sexual exploitation and trafficking [40]. Pandemic-induced poverty has also widened the gender poverty gap, pushing women into extreme poverty, as they earn less and hold less secure jobs than men [22,41]. The economic fallout for women has increased due to more unpaid care work, thereby compelling them to go back to traditional gender roles of more household and care workers [42].

Children are affected due to the pandemic and this is most visible in their health and education in various ways [43]. Children from marginalized sections have been the victims as inequalities in the teaching-learning system widened. Data show that 463 million children did not have access to the internet or digital devices for remote learning during the closure of schools [44]. Closures of schools have severely affected those children who rely on school-based nutrition programmes for their food and survival. Children suffering violence at home, refugee children, migrant children and children affected by conflict face appalling human rights violations and threats to their safety and well-being [45]. The additional stress and stigma that befall families struggling to cope have also impacted their children [45]. In the last two decades, there has been significant progress in the fight against child labour; however, the pandemic could significantly reverse this otherwise positive trend [46]. This reversal is because the crisis has enormously disrupted global education, and the lack of distance-learning solutions in many of the developing and underdeveloped countries has excluded children from online education for a very long duration. Furthermore, this trend has the potential to push millions of children into child labour [47]. Whilst the adverse socio-economic and financial impacts have fallen on the majority of households globally, there is significant inequality with some children impacted more severely, for example marginalized minority groups, disabled, street-connected and homeless populations, single or child-headed households, migrants, refugees, internally displaced persons, or people from conflict or disaster-affected areas, will be more vulnerable to child labour [48].

Beyond poverty and informality, the most explicit references to other vulnerable people and groups include older persons and people living with disabilities [49]. As the world struggles with an incomparable health crisis, older persons have become the topmost victims. The pandemic affected persons of all ages, yet older persons and those with underlying medical conditions tend to be at a higher risk of serious illness and death due to COVID-19 [50]. In the face of a life-threatening pandemic, especially during the first wave, many of the older persons faced challenges in accessing medical treatments and health care services for non-COVID ailments and chronic diseases. In developing countries, the prolonged lockdowns, weak health systems and healthcare facilities requiring out-of-pocket expenditure left millions of older people, especially those in the poorest groups, without access to basic health care, which ultimately increased their vulnerability to COVID-19 as well [51]. While older people often have been invisible in humanitarian action, the pandemic uncovered their exclusion. Older persons usually had to rely on multiple income sources, including paid work, savings, financial support from families and pensions. Additionally, for those older people living alone, isolation combined with other factors such as limited mobility creates greater risks [52]. Individuals living with disabilities represent 15% of the population [53], and their barriers related to accessing mobility, access to health services and appropriate communication have increased tremendously, which further increases their vulnerability [54]. The physical, social, economic and health impacts of COVID 19 on people with disabilities require empirical studies so that severity can be assessed and appropriate policies can be developed [55].

#### *3.2. Governance Issues*

The pandemic also put to test the efficiency and quality of governance and the political will of the leadership in each country. During a public health crisis, people naturally depend on their governments for security and support [56]. COVID-19 brought in a unique set of challenges to governments across the globe, such as a lack of post-crisis reconstruction and recovery, weak legal and institutional mechanisms, weak infrastructural facilities, including communication networks, a lack of systematic, periodic assessment and accounting of potential losses, and poorly managed financial, technical and human resources [57]. Spontaneous behavioural reactions such as generalized panic and rumours regarding the spread of COVID-19 were reported from across the countries and each country dealt with it using different levels of efficiency and effectiveness [58]. For example, in India, the most troubling aspect was the shortage of proper provision of safety nets (e.g., food safety) during the lockdown for the weakest and vulnerable sections of the population, which was tackled by providing free food grains and cash transfer support for three months [59]. The unprecedented pandemic situation has shown the inadequacies in

the global governance structure [31]. Moreover, the spread of fake news and misinformation was a major unresolved challenge for many of the democratic governments [60].

#### *3.3. Strategies for Solving Multiple, Interconnected Problems of COVID-19*

The WHO report on global surveillance for human infection with novel coronavirus highlights the importance of research studies to understand the viral transmission from animals and animal handlers, which will serve as evidence to prevent outbreaks similar to COVID 19 in the future [61]. To effectively respond to a public health emergency, the health system of the country must engage and step up preparedness activities with active involvement and leadership of the health department/ministry. Public health systems play a crucial role in planning health responses to respond and recover from the threats and emergencies introduced by pandemics. In various countries, fragmentation of health services has led to limited timely interventions and responses to health crises, which shows the need to have a strong coordination mechanism in place [62]. Public health emergency preparedness requires planning and intervention activities to prevent the spread of the virus, protect against other diseases and environmental hazards, promote and encourage health-seeking behaviours, respond to the crisis, assist communities in recovery, ensure quality and accessibility of the essential health services. Highly active surveillance is needed in all countries using the WHO-recommended surveillance case definition [63]. Furthermore, epidemiologic and surveillance activities would enable the public health systems to choose the most efficient ways to control the pandemic [64]. Non-pharmaceutical interventions based on supported physical distancing have a strong potential to lower the epidemic peak [65]. Priority should be accorded to certain areas, including assessment of the global health landscape; to accepting and recognizing epidemiological, environmental and economic crisis; to ensuring health regulations, such as tobacco control; to upgrading healthcare service delivery systems; and to ensuring innovative infection control, global research collaboration, universal health coverage, and public health surveillance. To support contact tracing, governments must consider expanding the use of information technology and digital initiatives to find high-risk areas [66].

The role of effective public health surveillance is crucial both in the short term and long term because the disease may remain in isolated pockets and regions even if it ceases to be a pandemic anymore. Surveillance informs about reality on the ground and provides insights for policymakers, which is essential [67]. Exploring and using web-based open tools to modernize data reporting can help provide newer, faster insights about COVID-19 controls [68]. COVID-19 surveillance in low/middle-income countries for a longer period is a real challenge due to a lack of resources, expertise, skills, people's attitude to tackling these issues technology transfer, financial assistance and capacity-building support is to be ensured [69].

The disease load of the pandemic is inequitably distributed among vulnerable populations [70]. People living in low- and middle-income countries have reduced capacity for self-protection (due to poor housing, sanitation and living conditions) [71] a high risk of food insecurity [72], a widened gap in health care access [73], loss of livelihoods, and a decrease in dietary intake and health care consumption [74]. Public policy needs to reorient federal, state and local governments to handle health equity issues sensibly [75]. The relevance of integrating public health efforts with broader public policy and acknowledging the role of social determinants of health is important [76]. Developing universal schemes for food assurance, minimum incomes, reforming unemployment insurance, and investment in community development will help to address health-inequity-related issues in the post-pandemic era [77].

COVID-19 is unlikely to be controlled or eliminated until there is global coverage of the population with effective vaccination. Vaccine development itself is not adequate; its mass production, affordability, global availability and acceptability in local communities are also important [78]. Strategies are needed to ensure affordability by handling Intellectual Property Rights issues and increasing production [79]. Long-term massive investment in the vaccination is needed; however, if the regular health budget is diverted for this, it will lead to long-term adverse consequences for general health indicators and development [80]. Increasing government revenue and getting grants and aid from donors and international loan providers are important [81]. Uneven distribution of vaccination is always a major challenge [82]; hence, vaccines should be distributed in stages, giving priority to older persons, high-risk individuals and people with co-morbidities [83]. The distribution must adhere to the WHO framework for allocating COVID-19 vaccines internationally based on need [84]. Vaccine hesitancy is prevalent in low-income and high-income countries alike, with sceptics found in all socioeconomic, religious and ethnic groups [85]. Culturally tailored health communication measures [86], community engagement [87] and a robust pharmacovigilance system [88] are important strategies for addressing vaccine hesitancy.

#### *3.4. Role of Multi-Stakeholders in Controlling the Pandemic and Promoting the Development*

COVID-19 presents a set of significant challenges to health care providers worldwide [89]. Given the complexity of the problem and the requirement of inter-sectoral collaboration, formal multidisciplinary working groups are recommended to offer relevant, effective and pragmatic solutions [90]. The pandemic is a complex phenomenon, with multiple determinants and impacts across all spheres of life. The pandemic experience serves as evidence for the need to adopt a comprehensive trans-disciplinary approach, including several experts, not only from medical sciences but also from engineering, political science, economics, humanities, psycho-social and demographic disciplines [91], as well as media that raises public awareness about health promotion and prevention [92]. The care of patients with COVID-19 can be optimized by collaborating with various multi-stakeholders to meet the demands that are required to combat the deadly disease. Multiple stakeholder engagement is critical to address the public health crises resulting from the pandemic, including but not limited to: aid donors [93,94], international aid networks, legislative and regulatory arms of the state, logistics organizations, private health care sectors [95,96], direct suppliers, media, social media [97–99], local aid networks, private insurance companies [100], military and para-military forces [101], government and inter-government organizations. Inputs of experts from the field of management, economics, environmental health, disaster management and other specialized disciplines to be incorporated in policy formulation based on inter-sectoral collaboration, which in turn can create programs and policies that are more efficient and feasible [90]. The support of patients, healthcare professionals and the wider community in addition to the government is equally important to address this health crisis [60].

#### *3.5. COVID-19 and Social Development*

The innovative, collaborative and strategic directions proposed to control the pandemic by slowing down transmission and reducing mortality associated with the pandemic are presented in Table 3.


**Table 3.** Strategies for COVID-19 and beyond.

**Table 3.** *Cont.*


#### **4. Future Research: Moving beyond the Transdisciplinary Framework and Study Limitations**

Trans-disciplinary health science research must be the prime approach to develop a universal response to COVID-19. Long-term research priorities must serve towards an evidence base for the public health system to plan or respond to future pandemics and to develop effective systems to reach out to the public [143]. The COVID-19 pandemic has been developed as a public health and developmental crisis for all countries, and this has revealed new challenges to the research community across the globe. Extensive research is needed to understand the COVID-19 crisis life cycle and its causes and consequences *(Recovery, Mitigation, Response and Preparation).* Revisiting datasets, redefining relevant methodologies, facilitating access to online resources and exploring culturally relevant approaches is critical at this juncture. The search for relevant information sources and trying to compile proper data of active as well as closed COVID-19 cases is an important task for health researchers. Research studies are needed to explore the interconnection of climate change to the development of the virus and to understand the possible environmental factors that could influence virus diffusion [144]. Comprehensive scientific studies needed to be initiated to explore COVID-19 s impact on human development, human happiness, the well-being of helping professionals, their families and others in the community. Synthesizing evidence more rapidly will help contribute towards provision of broad-ranging intervention guidelines and longer-term strategies for human happiness and well-being and social and economic recovery. Ensuring adequate quality research work, communicating thereof with multi-stakeholders and developing policy briefs for appropriate government action is a priority area. There is also a need to strengthen community-based crisis risk management, learn from the field with empirical evidence and replicate best practices. Transdisciplinary research is best suited to explore the new parameters that could be appropriate to explain COVID-19 s initial diffusion and its development as a pandemic [144].

#### **5. Recommendations**

The widespread prevalence of the infection and high causalities has made pandemic policies a high priority. As a response to control the pandemic, the WHO has recommended countries to develop preparatory policies to fight against the pandemic as well as address pandemic-induced developmental problems [145]. Developing appropriate COVID-19 control policies is a huge public health concern for all countries, and this requires combined inter-sectoral collaboration and government agreements through various coalitions [90]. The policy response should be two-fold: address present critical health and livelihood issues and suggest an approach to deal with the long-term issues the pandemic has introduced. The public health sector must take the lead for the whole of society, with a welfare approach to minimize the negative impacts of COVID-19 and help people restore the balance in their lives and livelihoods. This includes responding with appropriate public health emergency actions, identifying economic impacts, identifying and dealing effectively with misinformation spread about the disease [146]. Governments need to focus on providing authoritative information via multiple sources to ensure accurate data and appropriate social behaviour. Increasing transparency, ensuring proper restrictions, designing suitable prioritization guidelines about how to allocate scarce resources and making use of effective technologies are important [146]. To recognize the potential of psychological burnout from long hours of work and potential demoralization from persistent stress among health care workers is also an area that needs the urgent attention of policy framers. Vaccine and therapeutic investment, as well as research and development on COVID-19 control/elimination, is another key area. Governments need to strike a balance between protecting health and respecting human rights [146]. Identifying a new set of priorities and reworking national spending priorities will help to utilise available resources most efficiently and facilitate the return of normality in people's lives. Governments should address the long-standing challenges of health and nutrition of low-income households, strengthen food supply chains and empower women in food chains [147]. In response to the COVID-19 crisis, the International Labour Organization (ILO) has structured the four-pillar policy framework based on international labour standards to tackle the socio-economic crisis, stimulate the economy and employment, protect workers in the workplace, and rely on social dialogue for solutions [148].

#### **6. Conclusions**

The world is facing unprecedented challenges due to COVID-19, and hence pragmatic and innovative approaches are needed for pandemic management. To contain the spread of the virus, public health surveillance needs to be strengthened, through research, capacity building and action. Inter-institutional collaborations can help in enhancing the quality of surveillance, preparedness and capacity building during public health emergencies. Working closely with inter-regional and national public health and emergency management plans will help to control virus transmission and other risk factors. Since the pandemic has profound and long-term economic and social impacts, an integrated model for sustainable development, the delivery of training courses, and strengthening institutional mechanisms are essential for sustainable recovery and restoring normality in people's lives. The complex problems of pandemic threats have to be handled proactively by formulating innovative strategies and protocols to respond to similar outbreaks in the future. Furthermore, it is necessary to implement practical, evidence-based public policy measures and innovative approaches to deal with pandemic management, including developing strong linkages between strategic partners, alternative resource mapping strategies, a robust institutional and legal framework, and promoting health equity across economies.

**Author Contributions:** Conceptualization, S.P.; methodology, S.P., K.K., R.R.B.P., L.B. and H.S.M.; validation, K.K., L.R. and H.S.M.; data analysis and data synthesis, S.P., R.R.B.P., L.B., H.S.M., F.X.L.L.F. and K.R.N.; writing—original draft preparation, S.P., U.P., L.B. and R.R.B.P.; writing—review and editing, K.R.N., R.R.B.P., L.B., H.S.M., F.X.L.L.F. and L.R.; visualization, S.P.; supervision, S.P., K.K. and U.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **The Associations between Evacuation Status and Lifestyle-Related Diseases in Fukushima after the Great East Japan Earthquake: The Fukushima Health Management Survey**

**Zhichao Sun 1,2, Hironori Imano 1,3, Eri Eguchi 4, Fumikazu Hayashi 4,5, Tetsuya Ohira 4,5, Renzhe Cui 6, Seiji Yasumura 5,7, Akira Sakai 5,8, Michio Shimabukuro 5,9, Hitoshi Ohto 5, Kenji Kamiya 5,10 and Hiroyasu Iso 1,11,\***

	- <sup>11</sup> Institute for Global Health Policy Research, National Center for Global Health and Medicine, Tokyo 162-8655, Japan
	- **\*** Correspondence: iso@pbhel.med.osaka-u.ac.jp; Tel.: +81-6-6879-3911

**Abstract:** Background: This study aimed to investigate the association between evacuation status and lifestyle-related disease risks among Fukushima residents following the Great East Japan earthquake. Methods: Fukushima health management survey respondents were classified into non-evacuees, returnees, evacuees in lifted areas, and evacuees in banned areas. During a seven-year follow-up, 22,234 men and 31,158 women were included. Those with a history of diabetes, hypertension, or dyslipidemia at baseline were excluded. The odds ratios of risk factors (ORs) and 95% confidence intervals (CIs) for diabetes, hypertension, and dyslipidemia were calculated using a logistic regression model. Spatial autocorrelation of the prevalence of these diseases in the Fukushima area in 2017, was calculated to detect the disease prevalence status. Results: The risks of diabetes, hypertension, and dyslipidemia were higher in evacuees in banned areas than in non-evacuees; the multivariable ORs were 1.32 (95% CI: 1.19–1.46), 1.15 (1.06–1.25), and 1.20 (1.11–1.30) for diabetes, hypertension, and dyslipidemia, respectively. Returnees and evacuees in lifted areas had no increased risk of diseases. The area analyzed had a non-uniform spatial distribution of diabetes, hypertension, and hyperlipidemia, with clusters around Fukushima and Koriyama. Conclusion: Our findings imply the need for continuous support for evacuees in banned areas.

**Keywords:** evacuation; Great East Japan earthquake; disaster; disease prevalence status; cardiovascular and metabolic diseases

#### **1. Introduction**

The Great East Japan earthquake occurred on 11 March 2011, causing a large tsunami [1] and a severe accident at the Fukushima Dai-ichi Nuclear Power Plant [2]. These serious

**Citation:** Sun, Z.; Imano, H.; Eguchi, E.; Hayashi, F.; Ohira, T.; Cui, R.; Yasumura, S.; Sakai, A.; Shimabukuro, M.; Ohto, H.; et al. The Associations between Evacuation Status and Lifestyle-Related Diseases in Fukushima after the Great East Japan Earthquake: The Fukushima Health Management Survey. *IJERPH* **2022**, *19*, 5661. https://doi.org/ 10.3390/ijerph19095661

Academic Editor: Krzysztof Goniewicz

Received: 28 March 2022 Accepted: 5 May 2022 Published: 6 May 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

disasters resulted in extensive damage to the coastal area adjacent to the east of Fukushima, infrastructure destruction, and potential ultra-low-dose level radioactive pollution. Thus, many residents needed to evacuate, as implemented by the national and Fukushima Prefecture governments [3].

Evacuation affects lifestyle and has been associated with increased alcohol consumption [4], high smoking prevalence [5], and impaired sleep quality [6]. Lifestyle changes, such as those mentioned above, have a strong effect on lifestyle-related diseases. Moreover, changes in the living environment and socio-economic factors [7,8] could affect the mental health of the evacuees. People who were forced to leave their homes were more likely to develop post-traumatic stress disorder [9,10], and approximately 4.7% of the residents in the Fukushima Prefecture lost or changed their job [11]. Previous studies have also shown that evacuees had higher risks of diabetes, heart disease, and sudden cardiac death [12,13] than non-evacuees.

To date, restrictions have been lifted in 67.8% of the previously restricted areas [14], and the national and prefectural governments have encouraged the evacuees to return to their homes. However, some people remained reluctant to return, although the areas were cleaned and declared safe [15]. Therefore, people who continued to evacuate have been forced to live in temporary houses and face new interpersonal relationships.

Evacuation status may impact lifestyle and cardiovascular risk factors, such as diabetes, hypertension, and dyslipidemia. In this study, we hypothesized that the evacuees forced to live outside their original houses in banned areas may have a higher risk of diabetes, hypertension, and dyslipidemia, and that returnees and evacuees in lifted areas do not have these increased risks. We used the database affiliated with the Fukushima health management survey to test this hypothesis.

#### **2. Materials and Methods**

#### *2.1. Participants*

We used the following three databases from the Fukushima health management survey (FHMS) in 2017 [16]: comprehensive health checks, mental health and lifestyle survey, and basic survey. Comprehensive health checks included two sets of respondents as follows: (1) people in the evacuation zone specified by the government and (2) people outside of the evacuation zone in the Fukushima Prefecture. The evacuation zone comprised Iitate Village (mura), Kawauchi Village, Katsurao Village, Hirono Town (machi), Naraha Town, Tomioka Town, Okuma Town, Futaba Town, Namie Town, Minamisoma City, and Tamura City. The mental health and lifestyle survey included these 13 areas.

Figure 1a presents a flow chart of the longitudinal analysis used in this study, with a follow-up for up to 7 years. Among the 89,571 participants of the comprehensive health check database, we excluded 27,334 who were aged <20 years and 12,321 who did not participate in the mental health and lifestyle survey. A total of 49,916 participants were included in the analysis. Subsequently, we excluded participants with a history of diabetes (*n* = 5224), hypertension (*n* = 21,754), or dyslipidemia (*n* = 25,522) at baseline. At followup, there were 11,693 participants with diabetes, 8234 with hypertension, and 7021 with dyslipidemia who never responded. Finally, we analyzed 32,999 participants with diabetes, 19,928 with hypertension, and 17,373 with hyperlipidemia.

For the spatial analysis, 53,094 individuals were included in the 2017 total comprehensive health check database. We excluded 4204 individuals aged <20 years. Finally, 48,890 individuals were included in the analysis (Figure 1b).

(**b**)

**Figure 1.** Flow diagram of the participant selection process: (**a**) longitudinal analysis; (**b**) spatial analysis.

#### *2.2. Changes in Evacuation Status*

Figure 2 shows the changes in the evacuation areas in the Fukushima Prefecture in 2017, based on the information provided by the national and local governments [14,17]. As of 2017, areas that still have restrictions were labeled as Area1 (red color); those that have lifted restrictions, Area 2 (orange color); those with a history of voluntary refuge [17], Area 3 (yellow color); and those outside of the Fukushima Prefecture, Area 4 (green color).

**Figure 2.** Group design based on the history of the Fukushima evacuation area and caution area. Area 1: still difficult to return at the time of the deadline; Area 2: where the evacuation alerts have been lifted at the time of the deadline; Area 3: near the evacuation area or with a history of voluntary evacuation; and Area 4: all other areas.

Evacuees were defined as follows: those who had lived in Area 2 or 3 before the earthquake and evacuated from lifted areas until 2017 were defined as evacuees from lifted areas, and those who lived in Area 1 before the earthquake were defined as evacuees from banned areas. Non-evacuees were defined as all individuals living in Areas 3 and 4 who never changed their residences. Returnees were defined as individuals who lived in Area 2 before the earthquake, evacuated to Area 3 or 4 after the earthquake, and returned to their homes in Area 2 before 2017.

#### *2.3. Lifestyle Behaviors and Social Factors*

Smoking and drinking behaviors, sleep, physical activity, job change, and education level were obtained from the mental health & lifestyle survey data. We assessed the smoking status of the participants using the question, "Do you smoke?" with the following options: "non-smoker", "ex-smoker", and "current smoker". Those who selected "current smoker" were considered as current smokers. Participants' alcohol intake was assessed using the question, "Do you consume alcohol?" with the following options: "non-drinker (less than once per month)", "ex-drinker", and "drinker (once or more per month)". Those who selected "drinker (once or more per month)" were considered as current drinkers. Sleep quality was evaluated using the question, "Are you satisfied with the length of sleep for the past month?" with the following options: "satisfied" and "not satisfied". Physical activity level was assessed using the question, "Do you exercise regularly?" with the following options: "≥daily", "2–4 times/week", "weekly", and "almost never". Those who selected "≥daily", "2–4 times/week", or "weekly" were considered to have a physical activity frequency of at least once a week. Education level was assessed by the question, "What

is your last educational level?" with the following options: "elementary or junior high school", "high school", "vocational school or junior college", and "university or graduate school". Those who selected "university or graduate school" were considered to have received college or higher education. Change of job was assessed by the question, "Did you experience a change in work situation since the disaster?" with the following options: "yes" and "no". Psychological distress was evaluated using Kessler Psychological Distress (K6), and participants with a score of ≥13 were considered to have psychological distress.

Weight was measured in light indoor clothing without shoes, and height was recorded barefoot by well-trained staff. Weight and height measurements were obtained from comprehensive health check data. Body mass index (BMI) was calculated as weight (kg)/[height] (m)2.

#### *2.4. Onset of Diabetes, Hypertension, and Dyslipidemia*

The onset of diabetes mellitus, hypertension, and dyslipidemia was acquired from the comprehensive health check data. Hypertension was defined as systolic blood pressure (SBP) ≥ 140 mmHg, diastolic blood pressure (DBP) ≥ 90 mmHg [18], and/or the use of antihypertensive medication. Diabetes was defined as a fasting plasma glucose (FPG) level ≥ 126 mg/dL (7.0 mmol/L), random blood glucose (RBG) level ≥ 200 (11.1 mmol/L), HbA1c ≥ 6.5% [19], and/or the use of insulin injection or hypoglycemic drugs. Dyslipidemia was defined as plasma triglyceride (TG) level ≥ 150 mg/dL (fasting time), high-density lipoprotein cholesterol (HDL-C) level ≤ 40 mg/dL, low-density lipoprotein cholesterol (LDL-C) level ≥ 140 mg/dL [20], and/or the use of lipid-lowering agents.

#### *2.5. Addresses and Standardized Prevalence Ratios in the Fukushima Prefecture*

We used the current postal code from the basic survey data for the spatial analysis to ensure reliability. Diabetes, hypertension, and hyperlipidemia were defined based on the comprehensive health check database of the whole prefecture. The standardized prevalence ratios (SPRs) for diabetes, hypertension, and dyslipidemia were used to avoid distortion due to inappropriate age adjustment. The SPRs for diabetes, hypertension, and hyperlipidemia in each municipality in the Fukushima Prefecture were calculated compared to the 1985 Japanese standard population model. Municipality SPRs were calculated by dividing the municipality observed cases by the municipality expected cases [21,22].

#### *2.6. Statistical Analysis*

First, we calculated the age-adjusted mean values and prevalence of risk factors using analysis of covariance. Multiple linear regression was performed to compare the returnees, evacuees in lifted areas, and evacuees in banned areas with the non-evacuees.

Using the logistic regression model, age- and multivariable-adjusted odds ratios (ORs) and 95% confidence intervals (CIs) for diabetes, hypertension, and hyperlipidemia among the returnees, evacuees in lifted areas, and evacuees in banned areas, compared with the non-evacuees were calculated. The adjustment variables included age (continuous), BMI (quintiles), cigarette smoking status (never-smoker, ex-smoker, current smoker), alcohol consumption (non-drinker, ex-drinker, current drinker), physical activity (≥once weekly or <once weekly), sleep satisfaction (satisfied or not satisfied), change of job (yes or no), and educational status (elementary or junior high school, high school, vocational school or junior college, university or graduate school). Statistical analyses were conducted using SAS version 9.4 (SAS Institute, Inc., Cary, NC, USA). Two-tailed *p* values < 0.05 were considered statistically significant.

The global Moran's index [23] was used to analyze regional spatial autocorrelation to identify geographic clustering. Hotspot analysis (Getis-Ord Gi\*) [24] was used to determine the clusters. Hot spots represent a high-value spatial cluster of diabetes, hypertension, or dyslipidemia, whereas cold spots represent a low-value spatial cluster in the Fukushima Prefecture. Statistical significance was set at *p* < 0.05, and 90% CIs were dependent on the z < −1.65 or z > +1.65, whereas 95% CIs were dependent on the z < −1.96 or z > +1.96. All spatial analyses were conducted in ArcGis10.8.1 (Esri, Inc., Redlands, CA, USA).

#### **3. Results**

During a seven-year follow-up, 1822 participants had diabetes, 3609 had hypertension, and 4361 had dyslipidemia.

#### *3.1. Characteristics of Participants at Baseline*

Table 1 shows the age-adjusted mean values and characteristics at baseline according to the evacuation status. We found that 47.7% of the participants had been evacuated or were still evacuees. Compared with the non-evacuees, both evacuees in lifted areas and those in banned areas were younger and had a higher proportion of current smokers, current alcohol drinkers, dissatisfaction with sleep, change in their job, and university or graduate school education. Compared with the non-evacuees, the returnees were likely to have a lower average age and BMI and a higher proportion of dissatisfaction with sleep, change in their job, and university or graduate school education. Additionally, 11.6% of evacuees in banned areas had a K6 score of ≥13, which accounted for the highest proportion of individuals who had psychological distress.

**Table 1.** Characteristics of participants at baseline according to evacuation status (N = 49,916).


Difference from non-evacuees: \*\* *p* < 0.01; \*\*\* *p* < 0.001.

#### *3.2. Associations between Evacuate Status and Diabetes, Hypertension, and Dyslipidemia*

Table 2 presents the age- and multivariable-adjusted odds ratios (ORs) and 95% confidence intervals (95% CIs) for diabetes, hypertension, and dyslipidemia for the returnees, evacuees in lifted areas, and evacuees in the banned areas. The ORs for diabetes, hypertension, and dyslipidemia for evacuees in the banned areas were significantly higher than those for non-evacuees, and these associations remained statistically significant even after adjusting for confounders. The multivariable ORs (95% CIs) were 1.35 (1.22–1.51) for diabetes, 1.14 (1.05–1.24) for hypertension, and 1.22 (1.13–1.32) for dyslipidemia. The ORs for diabetes, hypertension, and dyslipidemia were higher in returnees than that in non-evacuees, albeit not statistically significantly. There was no statistically significant association between the evacuees in lifted areas and the non-evacuees. With additional adjustment for psychological distress, the results still showed the same associations. Multivariable ORs (95% CIs) were 1.35 (1.21–1.50) for diabetes, 1.14 (1.05–1.24) for hypertension, and 1.22 (1.13–1.32) for dyslipidemia.

Gender-specific analyses (Table 3) showed similar associations, except for hypertension in men. The multivariable ORs (95% CI) for diabetes, hypertension, dyslipidemia were 1.33 (1.15–1.55), 1.08 (0.95–1.23), and 1.31 (1.16–1.48) among male evacuees in banned area and 1.38 (1.19–1.61), 1.20 (1.08–1.35), and 1.21 (1.09–1.34) among female evacuees. Additional adjustment for psychological distress also showed the same associations. Multivariable ORs (95% CIs) for diabetes, hypertension, and dyslipidemia were 1.33 (1.15–1.54), 1.08 (0.94–1.23), and 1.31 (1.16–1.48), respectively, among male evacuees in banned areas and 1.38 (1.18–1.60), 1.20 (1.08–1.35), and 1.20 (1.09–1.33) among female evacuees in banned areas.


**Table 2.** Age-adjusted and multivariable odds ratios of diabetes, hypertension, and dyslipidemia according to evacuation status.

CI, confidence interval; OR, odds ratio. \* *p* < 0.05; \*\* *p* < 0.01;\*\*\* *p* < 0.001. § Adjust for age, body mass index, smoking status, alcohol consumption, sports time, sleep quality, education level, and change of job. §§ Adjusted further for psychological distress.

#### *3.3. Spatial Distribution Characteristics*

The global spatial autocorrelation showed that the prevalence of diabetes, hypertension, and hyperlipidemia was positively spatially autocorrelated in Fukushima (Supplementary Table S1). The global Moran's indexes for diabetes, hypertension, and dyslipidemia were 0.17, 0.16, and 0.34, respectively. The administrative region around the Fukushima and Koriyama cities were determined as clusters (Figure 3). However, Iwaki City is in the lower right corner of Fukushima Prefecture, so the spatial pattern may lack of significance.

*IJERPH* **2022**, *19*, 5661

**Table 3.** Gender-specific age-adjusted and multivariable odds ratios of diabetes, hypertension, and dyslipidemia according to evacuation status.


 *p* < 0.05; *p* < 0.01; *p* < 0.001. Adjust for age, body mass index, smoking status, alcohol consumption, sports time, sleep quality, education level, and change of job. Adjustedfurther for psychological distress.

(**c**)

**Figure 3.** Hot spot analysis of spatial prevalence of lifestyle-related diseases among survey participants: (**a**) Spatial pattern of diabetes; (**b**) Spatial pattern of hypertension; (**c**) Spatial pattern of dyslipidemia.

#### **4. Discussion**

This study revealed that evacuees in banned areas had a higher risk of diabetes, hypertension, and dyslipidemia than non-evacuees, whereas returnees and evacuees in lifted areas did not have increased risks. These associations remained significant even after

adjustment for selected lifestyles, education level, and change of job. Poor lifestyle factors including smoking, heavy alcohol consumption, physical inactivity, and inadequate sleep have been proven to enhance the incidence the lifestyle-related diseases [25,26]. Factors related to socioeconomic status such as low education level and change of job have also been confirmed as risk factors for the incidence of cardiovascular and metabolic diseases [7,27]. In addition, a high-high cluster of diabetes, hypertension, and dyslipidemia around the cities of Fukushima and Koriyama was noted. This study is the first to evaluate the risk of lifestyle-related diseases among returnees and evacuees in the lifted areas, and evacuees in the banned areas.

We attempted to explain why the evacuees in the banned areas had a higher risk of diabetes, hypertension, and hyperlipidemia than the other groups and the causes of spatial clustering in the discussion below.

First, in our study, the excess risks of diabetes, hypertension, and dyslipidemia among evacuees in banned areas were not altered after adjustment for psychological distress. However, this result in 2017 did not negate the possibility that that psychological distress confounded or mediated the excess risks probably because mental stress may temper over time [28].

Mental stress has been associated with an increased risks of diabetes [29], hypertension [30], and dyslipidemia [31,32]. Moreover, the incidence of diabetes increased [33,34] among evacuees immediately following the disaster. The hypothalamic–pituitary–adrenal axis [35,36] increases circulating cortisol levels, and under chronic stress conditions, the pituitary gland secretes vasopressin [35], which could affect glucose and lipid metabolism, leading to diabetes, hypertension, and dyslipidemia.

Second, diverse socio-economic factors may have influenced the incidence of lifestylerelated diseases. Evacuees in banned areas were closer to the center of the accident, were more vulnerable to the negative impact of the accident, and had no choice but to evacuate. Sugimoto et al. showed that long-term evacuation could lead to a poor perceived health status [35]. In addition, a recent report reported that evacuees in the banned area had less communication with others regarding their daily lives than those in the lifted areas [36]. These factors may have increased the risk of lifestyle-related disease onset.

Furthermore, the evacuees in the banned areas needed to leave their own houses and lose their material possessions and jobs, leading to a loss of purpose in life. Unemployment has been considered as a common factor that could increase the risk of delayed mental illness [37–39]. In addition, house damage, tsunami experience, nuclear power plant accident experience, and loss of family, realty, and close friends were associated with increased mental stress [40]. Moreover, we assumed that evacuees in the banned areas who were eager to return to their home but were unable to do so have a greater burden; thus, their risk of developing lifestyle-related diseases may be higher.

According to our findings, the prevalence clusters of hypertension, diabetes, and dyslipidemia were mainly located around the cities of Fukushima and Koriyama. Fukushima City is the provincial capital, whereas Koriyama City is one of the most populous commercial cities in the Fukushima province. Therefore, collective infrastructural resources are concentrated in Fukushima and Koriyama [41]. Additionally, after the disaster, these two cities, and the surrounding areas closest to the disaster site, quickly established emergencyrelevant infrastructure and accepted many evacuees [42]. Therefore, this could partially explain why the spatial pattern of diabetes, hypertension, and dyslipidemia prevalence in the Fukushima and Koriyama cities were different from other cities.

Compared with other similar studies [13,43–45], this study has the following salient features. First, it analyzed a large population-based cohort, which not only included the residents in the affected areas of the Great East Japan earthquake, but also those throughout the entire Fukushima Prefecture. Second, over 70% of participants were followed-up for seven years from 2011–2017. Third, we adjusted for several potential confounders, including lifestyle and socioeconomic factors.

However, this study had some limitations. First, each participant may not have taken the comprehensive health checks and mental health and lifestyle surveys conducted annually. Therefore, we could not assess the impact of lifestyle changes on the incidence of diabetes, hypertension, and dyslipidemia. Second, we did not have data on the proportion of people who evacuated outside the Fukushima Prefecture and the prevalence of diseases in cities, towns, and villages in other prefectures around the Fukushima Prefecture. Third, regarding the spatial analysis, we only examined the prevalence of diabetes, hypertension, and dyslipidemia in 2017. Therefore, we could not examine the dynamic clustering process of each region. Lastly, the lifestyle parameters were based on a self-reported questionnaire and liable to misclassification.

Nevertheless, this is the first study to describe the prevalence and incidence of diabetes, hypertension, and dyslipidemia in the Fukushima area using both a cross-sectional design for the spatial dimension and a longitudinal design for the temporal dimension.

#### **5. Conclusions**

During a 7-year follow-up after the Great East Japan earthquake, evacuees in the banned areas had a higher incidence of diabetes, hypertension, and dyslipidemia than non-evacuees. Our findings imply the importance of continuous support for the prevention of lifestyle-related diseases for the evacuees in banned areas.

**Supplementary Materials:** The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/ijerph19095661/s1, Table S1: Global Moran index of the spatial distribution of the prevalence of lifestyle-related diseases by administrative division among examinees.

**Author Contributions:** Z.S., R.C., H.I. (Hiroyasu Iso) and T.O. contributed to the study design; Z.S., E.E., F.H., T.O., S.Y., M.S., A.S., H.O. and K.K. were responsible for the data collection and overseeing the study procedures; The analysis was conducted by Z.S. and F.H.; The manuscript was written by Z.S.; H.I. (Hironori Imano), E.E., F.H., T.O., R.C., S.Y., A.S., M.S., H.O., K.K. and H.I. (Hiroyasu Iso) made significant contributions to the critically interpreted the results and provided intellectual content. All authors have read and agreed to the published version of the manuscript.

**Funding:** This survey was supported by the Japan National Health Fund for Children and Adults Affected by the Nuclear Incident; the Institute for Transdisciplinary Graduate Degree Programs of Osaka University, the Projects for Leading Graduate Schools on Interdisciplinary Program for Biomedical Science; the Network-type Joint Usage/Research Center for Radiation Disaster Medical Science, the Projects for Research on risk communication regarding radiation disasters; the Japan's Science and Technology Agency, Projects for Support for Pioneering Research Initiated by the Next Generation (grant number JPMJSP2138); and Research Project on Health Effects of Radiation organized by the Ministry of the Environment, Japan.

**Institutional Review Board Statement:** The study protocol was approved by the ethics committees of the Fukushima Medical University (IRB, approval number: 20018) and the Osaka University (IRB, approval number: 1319 and 2148). The target of this observational study was residents in the Fukushima Prefecture at the time of the disaster, and no intervention was implemented during the observation process. The study was conducted in accordance with the Declaration of Helsinki.

**Informed Consent Statement:** Informed consent was obtained from the community representatives to conduct an epidemiological study based on the guidelines of the Council for International Organizations of Medical Science.

**Data Availability Statement:** The datasets analyzed during the present study are not publicly available because the data from the Fukushima Health Management Survey belongs to the government of Fukushima Prefecture and can only be used within the organization.

**Acknowledgments:** We thank all the member who belongs to the Fukushima Health Management Survey for their support. The findings and conclusions of this article are solely the author's responsibility and do not represent the official views of the Fukushima Prefecture Government or the Japanese Government.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Unmanned Aerial Vehicle in the Logistics of Pandemic Vaccination: An Exact Analytical Approach for Any Number of Vaccination Centres**

**Adnan Benayad 1,2,\*, Olaf Malasse 3, Hicham Belhadaoui 1,2 and Noureddine Benayad <sup>4</sup>**


**Abstract:** While the development and manufacture of pandemic vaccines is a daunting task, the greatest challenge lies in how to deliver these vaccines to billions of people around the world. This requires an efficient strategy of deliveries, at constrained costs and deadlines. This paper proposes an exact analytical approach and operational strategy to the logistics of any pandemic vaccination efforts, applicable both to sparsely populated areas or deficient infrastructure, and to very dense urban fabrics where mobility is highly constrained. Our strategy consists in dividing the territory concerned into zones and districts in a concentric way. We opt for the use of unmanned aerial vehicles to free ourselves from land constraints. This involves serving, from a logistics centre (central depot), any number n of vaccination centres, while optimizing costs and deadlines. We have determined all equivalent and optimal flight path plans for a fixed and optimal number of drones, which depend on domain D(d); d being the demand of vaccination centers. The analysis of the results led us to define what we will call the "degeneracy of domain D". All our results are expressed as a function of the parameter n.

**Keywords:** pandemic vaccination; exact analytical approach; unmanned aerial vehicle (UAV); drone delivery; route planning problem; optimal flight path; equivalent graphs; degeneracy

#### **1. Introduction**

Until recently, Unmanned Aerial Vehicles (UAVs) or drones have primarily been used in the military. Recently, they are becoming more present in many civilian sectors. This will open new possibilities for further research and development of UAVs. They are considered as one of the technological innovations which may trigger a revolutionary reshaping of transportation industry, since they have the potential to significantly reduce the cost and time required to deliver packages. By performing these tasks autonomously, drones may be faster than traditional delivery vehicles such as trucks since they are not limited by established infrastructure such as roads, and generally face less complex obstacle avoidance scenarios which complies with current trends in the transport industry [1].

It is noteworthy that a lot of pilot projects have been launched to exploit the potentials of drones in logistics applications. Examples of large organisations experimenting with drones are Google, DHL, and Amazon Indeed, in 2013, Amazon announced Prime Air [2,3], a service that utilizes multirotor drones to deliver packages from Amazon to customers. German logistics company Deutsche Post DHL also started its Parcelcopter project in 2013; the Parcelcopter has transported medicine to the island of Juist in the North Sea [4]. Google revealed Project Wing in 2014 to produce drones that can deliver larger items than Prime

**Citation:** Benayad, A.; Malasse, O.; Belhadaoui, H.; Benayad, N. Unmanned Aerial Vehicle in the Logistics of Pandemic Vaccination: An Exact Analytical Approach for Any Number of Vaccination Centres. *Healthcare* **2022**, *10*, 2102. https:// doi.org/10.3390/healthcare10102102

Academic Editors: Amir Khorram-Manesh and Krzysztof Goniewicz

Received: 11 August 2022 Accepted: 11 October 2022 Published: 20 October 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Air and Parcelcopter [5]. A startup called Matternet has partnered with Swiss Post to test a lightweight package delivery quadcopter [6]. Next to large-scaled projects of multi-national firms, also smaller-scaled projects of drone delivery systems have been successfully put into practice [7].

Non-military UAVs come in various shapes and sizes and typically contain a main airframe, navigation system and propulsion systems [8]. In medicine we use two primary types (i) fixed-wing aircraft and (ii) helicopter-like drones with single or multiple rotors.

For logistical applications, the speed, payload capacity and radius of operation are the most important technical parameters. They vary greatly among different drone models. Primarily models with payload capacity up to 5 kg are used [9,10]. However, also heavyload UAVs are available with a payload capacity of up to 40 kg [11]. Drones, such as those produced by Zipline (Half Moon Bay, CA, USA), can fly at a speed of up to 128 km/h (80 mph) and have a range of 160 km (99 miles) round trip [12].

Developments in numerous technologies have enabled the above organizations to improve drone deliveries. Carbon fibre manufacturing costs have decreased significantly over the last years [13,14], enabling the development of strong, lightweight airframes. Lithium polymer batteries, known by their relatively high energy density [15] have improved the flight times of the drones compared to alternative technologies such as nickel-cadmium and nickel-metal hydride. UAVs typically use GPS to determine their location, and they are also able to take advantage of DGPS and localization techniques [16,17] to improve accuracy. Obstacles can be avoided through many techniques such as LIDAR and image processing [18,19]. Architectures and protocols have been developed that enable drones to form ad-hoc networks and to wirelessly communicate with other entities [20,21].

Other technological issues to be considered in logistical UAV applications are the launching and landing concept in addition to the autonomous control capability. Meanwhile, most commercial UAV models also provide fully automatic launching stations [22]. For B2C concepts, however, the UAV must be able to land on 'rough' ground. Further, some detachment technology like ropes (Flirty, Google) or parachutes (Zipline) could be available. In a B2C application scenario, it is reasonable to assume that UAVs must wait hovering until all prerequisites for detaching the cargo are fulfilled (e.g., waiting for the customer's approval or a clear detachment area).

Drones' systems have also been reported in other practical applications in emergency and disaster management situations where the crucial feature is the drone's ability to travel directly between several points of interest [23] over hazardous terrain during a crisis. These include intelligence, surveillance and reconnaissance (ISR) missions to visit a n set of locations [24]; and in emergency aid in order to reduce the worker's exposure to danger and also for emergency response in the event of forest fires, oil spills, and earthquakes [25]. UAVs equipped with cameras allow for viewing disaster scenes promptly, collecting critical data including aerial photograph, air quality or radiation levels. They can deploy wireless sensors to provide immediate updates on the event to the teams on the ground. On the other hand, in the healthcare sector, especially in developing countries [26], UAVs have already been used in different aspects, including transfer of blood product. They can also be used to transport diagnostic samples and various medical purposes [8,27]. Finally, we note that such drones are also used in agriculture (monitoring crop production), construction (surveying land), industry (warehouse management), public safety (law enforcement and traffic surveillance), and environmental conservation efforts (deforestation monitoring),

In a world where logistics has become a vital function, as we were able to verify during the COVID-19 health crisis, but where the margins of the various players in the supply chain are increasingly tight and prices constantly drawn down, the drone is a solution to consider and seriously study for all those who want to increase their operational efficiency and stand out for their quality of service.

The purpose of the paper is to offer an exact analytical approach and operational strategy to the logistics of any pandemic vaccination effort. Our study gives an answer to the following question: How to use drones in order to deliver pandemic vaccines to large areas (densely populated city or sparsely populated rural region) whatever the number of the population living there. Indeed, this paper primarily studies the route planning problem of the UAVs during distribution. The application scenario is the vaccines delivery from the distribution centre to the vaccination centres, and to determine all equivalent and optimum flight path plans for drones that need to serve multiple positions for any number of vaccination centres.

The structure of this paper is as follows. Section 2 provides a review on the relevant literature. In Section 3, we formally introduce the strategy, hypotheses and used notations. Section 4 describes the drone routing problem for fixed numbers of vaccination centres. In Section 5, we provide a generalization of the drone routing problem, i.e., for any number of vaccination centres. This problem leads us to define what can be called "the degree of degeneracy" of the vaccination centres demand. Section 6 concludes the paper.

#### **2. Literature Review: Use of Drones in Healthcare**

Research on employing drones in delivery operations has gained a lot of attention in recent years. There is an exploding body of literature on potential application scenarios concerning this subject. An extensive overview about civil applications of UAVs can be found in reference [28].

Drones have been used in several sectors of healthcare. Preliminary reports have indicated the feasibility of drone related transfer of biological samples (for instance, blood product) during short flights at room temperatures or colder with no significant influence on the accuracy of routine chemistry, haematology and coagulation analyses [29,30]. In this sector, we must notice that Rwanda was the first country to successfully use drones into health services at the national level. A drone delivery programme also known as 'Uber for blood' was launched in 2016. It uses battery-powered fixed-wing drones designed and built by Zipline capable of flying up to 150 km in a round trip and carrying up to 1.5 kg of blood. We note here that Rwandan patients have never received blood quickly and so efficiently: Indeed, blood delivery times have plummeted from approximately 4 h to only 15–45 min in remote areas. More than 18,000 life-saving delivery flights containing blood products were carried out in August 2019 [31].

In 2016, UNICEF and the Government of Malawi initiated an important programme in order to explore whether sample transportation by UAV is a cost-effective intervention to reduce time-to-result for human immunodeficiency virus testing in infants [32]. Drone have been also used in another sector of healthcare. In Papua New Guinea, where the prevalence of tuberculosis is one of the highest in the world (nearly 6/1000 population/year), drones were used to transport sputum samples of individuals with suspected tuberculosis from dispersed health centres to Kerema General Hospital, which circumvented the need to use road transport that was hampered during the rainy months [33].

On the hand, in 2017, Switzerland paved the way for the transport of specimens by drone in Europe by authorizing flights of autonomous drones for healthcare services over cities at any time. Swiss Post and Matternet have developed a medical transport network using quadcopter drones (20-km range, average speed 36 km/h, 2-kg maximum payload), with more than 3000 successful flights in Lugano, Bern and Zurich in April 2019 [27,34].

A drone programme has also been successfully implemented in Tanzania, a country with one of the highest maternal mortality rates in the world (556 deaths/100 000 deliveries). The drones were much faster than ground transportation, delivering on-demand blood, vaccines, and antiretroviral and malaria drugs via biodegradable parachutes to more than 1000 health facilities [35].

In April 2019, Gavi, the Vaccine Alliance, announced the launch of the largest drone healthcare project. Delivery of blood, medicines and vaccines is now available for 2000 health facilities serving 12 million people across Ghana. Distribution centres can deliver up to 600 on-demand drone transports per day with potential for further expansion to up to 2000 flights/day [36].

The economic and operational value concerning vaccine deliveries was recently assessed using a computational model [7]. Compared with traditional land transport, drone delivery increased vaccine availability and decreased costs (\$0.05 to \$0.21 per dose administered), proving that drones are cost-effective and useful in a variety of circumstances and settings if used frequently enough to overcome the system installation and maintenance costs [37]. We note that drone delivery has been successfully piloted in Vanuatu (a Pacific archipelago) where most villages are not easily reachable and often have no electricity to store vaccines, leaving nearly 20% of Vanuatu's 35,000 children under 5 years not fully vaccinated [37].

The World Health Organization has designated COVID-19 as a pandemic. Currently, over 140 million cases of COVID-19 have been confirmed worldwide, including more than 3,000,000 deaths. There is a dire need for therapeutics and vaccines to fight such pandemic. Distributing an effective vaccine to billions of people around the world is likely the greatest logistical challenge since the Second World War. First, to satisfy the high-demands during the COVID-19, some models have been developed [38] in order to increase the production of vaccines. On the other hand, they should be transported, from the manufacturing sites to distributors. These latter must deliver the vaccines to vaccination centres, which have to be adequately and uniformly distributed in urban and rural areas. This is not an easy task, especially if we know that maintaining the cold chain will be a crucial issue for such vaccines, which poses a significant problem in many parts of the world. Low temperatures must be maintained whether vaccines are being delivered to densely populated cities or sparsely populated rural areas. We must note that the pandemic vaccines have to be stored within appropriate and efficient conditions. This is the health guidelines state that even small deviations can render a vaccine ineffective. According to a 2019 report by the International Air Transport Association (IATA), approximately 25% of vaccines shipped are at risk due to poor temperature management in transportation vehicles. The report estimates that the associated damage costs the healthcare industry more than \$34 billion annually. For the people and economies that depend on the prevention of COVID-19, inefficient cold chain management will be particularly costly. Thus, healthcare distributors and providers must operate in a specialized, temperature-controlled supply chain. It is worthy to note that in the context of the COVID-19 pandemic that Zipline is deploying its ingenious logistics. Faced with problems relatively identical to those of Rwanda, the Ghanaian government has also chosen to call on the Californian start-up for the delivery, initially of tests, then now of Covid vaccines. About 2.5 million doses are expected to be delivered in Ghana using these drones [31]. Not only does this make Ghana the first country in the world to deploy drones nationwide for the delivery of COVID-19 vaccines, but it is also a mammoth effort to ensure equitable access and enable Ghana to use fully its healthcare infrastructure to deliver vaccines," Zipline CEO Keller Rinaudo said in a statement.

#### **3. Strategy, Hypotheses and Notations**

#### *3.1. Strategy*

In this paper, we are interested in the use of drones in logistics of any pandemic vaccination. The strategy we adopt to vaccinate the population of a given territorial area (urban or rural) is clearly shown in Figure 1. Indeed,


**Figure 1.** Localization of all vaccination centres belonging to the concerned territorial area.

#### *3.2. Hypotheses*

In order to perform such vaccination operation using drones, we have to study the route planning problem of the UAVs distribution. To this end, we consider the following assumptions:


#### *3.3. Notation*

We define the different sets needed for modelling the problem in addition to the parameters and variables.


#### **4. Drone Routing Problem for Fixed Number of Vaccination Centres**

*4.1. Optimum Number of Drones and Vaccination Centre Demands*

Before giving our general formulation of logistics distribution for any number n of vaccination centres and valid for any zone, we give in this section, a detailed presentation of the model in the case of small, fixed values of n = 5,6,7,8, and 9.

First, we represent the correlation between the optimum number of drones necessary to use for logistics distribution and the needs of the vaccination centres. The cases n = 7,8, and 9 are presented in Table 1. The other cases corresponding to n = 5 and 6, are presented in Appendix A.

**Table 1.** Domains of d, corresponding graphs and lengths *L* (*n, N*) of the paths travelled by the set of optimum number of drones necessary for the logistics distribution, when zone contains n = 7, 8, and 9 vaccination centres, respectively.




In the first column, we have considered all possible ratios d/C between the demand d of each vaccination centre and the load capacity C of the drone. In the second column, we indicate the maximum number k1(d) of vaccination centres that one drone can serve. In the third column, we note optimum number N of drone we should use for each logistics distribution, according to the various ranges of vaccination centres demands. In the fourth column, we represent the exact graphs calculated in the frame of our approach.

In all Tables, we represent the length *L* (*n, N*) of the paths travelled by the set of the optimal number of drones necessary for logistics distribution. Its general expression for any n and N is given by the following relation:

$$L(\mathbf{n}, \mathbf{N}) = (\mathbf{n} - \mathbf{N})a\_{\mathrm{ll}} + 2\mathbf{N}r\_{\mathrm{ll}} \tag{1}$$

where *an* is the distance between two nearest vaccination centres belonging to the same n-polygon (zone) and *rn* is its circumradius. They are given by:

$$a\_n = 2(2\mathbf{n} - \mathbf{7})\sin\left(\frac{\pi}{\mathbf{n}}\right)r$$

$$r\_n = (2\mathbf{n} - \mathbf{7})r$$

It is important to notice that this length is constant for any fixed N and therefore it does not depend on the corresponding intervals, although these latter correspond to various graphs.

In order to give an elegant formulation of the results demonstrated in the above Tables, we represent in Figure 2, the variation of optimum number N of drones as function of vaccination centre demands. This is done for different number n of centres. As is observed in these figures, this variation can be described by a function which can be called "ceiling function with unequal steps".

**Figure 2.** The variation of optimum number N of drones as function of vaccination centre demands, for n = 7, 8, and 9.

The other cases corresponding to n = 5 and 6 are presented in Appendix A.

#### *4.2. Degeneracy of the Domains of Vaccination Centres Demands*

In the rest of our investigation, we are interested in the study of the domains (intervals) of d/C where the set of vaccination centre demands, belonging to the same zone, are served by a fixed optimum number N of drones.

It is worthy to notice an interesting behaviour related to the topology of the graphs. It concerns the existence of multiple graphs for a defined range of vaccination centre demands satisfying a well-defined maximum number of centres. For instance, this is observed in the case N = 3 for n = 7 and 9 when d/C belongs to ranges  1 4 , 1 3 and  1 5 , 1 4 , respectively. The corresponding variety of graphs can be called "equivalent graphs" in the sense that they have the same length of paths taken by the N drones but different topologies. Therefore, they use the same energy consumption during logistics distribution. This behaviour can

be called the degeneracy of the corresponding domain. In the present paper, we focus our study to two cases, namely: (i) N = 2 and (ii) N = 3.

In Figures 3 and 4, we draw for various zones which contain respectively different centres (n = 12, 13, and 15), the set of possible graphs corresponding to the various domains D of d/C.

(i) For N = 2, we obtain

(**c**)

**Figure 3.** Set of possible graphs corresponding to the various domains of d/C for N = 2, (**a**) n = 12, (**b**) n = 13, and (**c**) n = 15.

As is observed from Figure 3, we note that, in every range of d/c, there is one and only one graph. We note that all graphs corresponding to N = 2 have different topologies which depend on the maximum number of vaccination centres that can be satisfied by one drone.

(ii) For N = 3, we obtain

**Figure 4.** Set of possible graphs corresponding to the various domains of d/C for N = 3, (**a**) n = 12, (**b**) n = 13, and (**c**) n = 15.

(**c**)

In Figure 4, we represent all possible graphs for N = 3, according to each domain of vaccination centre demands. We note the existence of multitude graphs in well-defined domains of d/C. For instance, in the case (n = 15, N = 3), when d/C belongs to <sup>1</sup> <sup>8</sup> <sup>&</sup>lt; *<sup>d</sup> <sup>C</sup>* <sup>≤</sup> <sup>1</sup> 7 , we have 4 equivalent graphs which they have the same global length and therefore the same "global" cost and the same delivery time.

In order to give a precise description to the above interesting behaviour, we suggest a new nomenclature describing this variety of equivalent graphs. To this end, we introduce the following definition: We define the degeneracy of a domain D(*α* < *<sup>d</sup> <sup>C</sup>* ≤ *β*) by the number of equivalent graphs existing in the specified range (*α* < *<sup>d</sup> <sup>C</sup>* ≤ *β*). In addition to the degeneracies expressed in Figure 4, we have calculated the degeneracy of domains corresponding to N = 3 for zones containing large numbers of vaccination centres (n = 18, 21, 24, and 27). Below, we give their degrees and corresponding graphs.


#### **5. Drone Routing Problem for Any Number of Vaccination Centres**

In this section, we reformulate our model for any number (n ∈ IN) of vaccination centres. The optimum number of drones that can be used to perform the distribution is N = 2 and 3.

Consider a zone and let n be the number of vaccination centres located on the sites (vertices) of the regular n-polygon inscribed in that zone. The drone's platform is situated on the centre of the circumcircle of the polygon.

#### *5.1. General Expressions of Demand Domains and Their Corresponding Graphs*

First, let us find for any fixed n, the set of domains D (*α* < *<sup>d</sup> <sup>C</sup>* ≤ *β*) defined in the previous section. The domains concerned by our generalization are those where the vaccination centres are served by an optimal number of drones equal to 3 (N = 3). To this end, it should be noted that these domains depend on the parity of n.

(a) For odd numbers n ≥ 3

The possible domains and corresponding graphs are given by:


where *p* is the smallest integer value satisfying the following inequality:

$$3\left(\frac{n-1}{2} - p - 1\right) < \text{n.}$$

It follows that *p* is given by:

$$p = flow\left(\frac{n-9}{6}\right) + 1\tag{2}$$

which can be expressed by the following expression:

$$p = \begin{cases} \frac{n-9}{6} - \frac{1}{\pi}arccot\left[\cot\left(\frac{n-9}{6}\pi\right)\right] + 1, & n \neq 12k + 15/k \in IN\\ \frac{n-9}{6} + 1, & n = 12k + 15/k \in IN \end{cases} \right\}$$

(b) For even numbers n ≥ 6

We note that for n = 2 or 4, there is no domains and equivalent graphs corresponding to N = 3. For even numbers n ≥ 6, the possible domains *D* and corresponding graphs are given by:


where *q* is the smallest integer value satisfying the following inequality:

$$3\left(\frac{\mathbf{n}}{2} - q - 1\right) < \mathbf{n}$$

It follows that q is given by:

$$q = flow\left(\frac{\mathbf{n}}{6}\right) \tag{3}$$

which can be written in the following expression:

$$q = \begin{cases} \frac{\text{n}}{6} - \frac{1}{\pi} \text{arccot} \left[ \cot \left( \frac{\text{n} \pi}{6} \right) \right] , \text{ n} \neq 12k + 6/k \in IN\\ \frac{\text{n}}{6} \text{ } & \text{n} = 12k + 6/k \in IN \end{cases} \text{\(\text{n}\)}$$

We note that for any odd (or even) n, each domain Di (*Di*) corresponds to certain number of equivalent graphs. This later represents the degeneracy of the domain Di (*Di*).

#### *5.2. General Expressions of the Domain Degeneracy*

The detailed analysis of the domains and their corresponding graphs presented in Section 5.1: (a) and (b) of this section, allow us to establish general expressions of their degeneracy for both odd and even numbers n of vaccination centres. We have indicated that the defined degeneracy deg(n, N, D- (or *Di*)) depends on four sets covering all possible integer values. Thus,

$$\text{(i)}\quad \text{For } n \in \{3 + 4k/\ k \in IN\}$$

$$\text{deg}(\mathbf{n}, \mathbf{N} = 3, \,\mathrm{D}\_{\ell}) = \begin{cases} \frac{\mathrm{u}}{4} - \frac{3}{4} (2\ell + 1) + 1, \,\mathrm{if}\,\,\ell \text{ is even} \\\frac{\mathrm{u}}{4} - \frac{3}{4} (2\ell + 1) + \frac{1}{2}, \,\mathrm{if}\,\,\ell \text{ is odd} \end{cases} \tag{4}$$

D denotes the domain: <sup>1</sup> *<sup>n</sup>*+<sup>1</sup> <sup>2</sup> −- < *<sup>d</sup> <sup>C</sup>* <sup>≤</sup> <sup>1</sup> *<sup>n</sup>*−<sup>1</sup> <sup>2</sup> −where

$$\ell \in \left\{ 0, 1, 2, 3, \ldots, floor \left( \frac{n-9}{6} \right) + 1 \right\} \tag{5}$$

(ii) For *n* ∈ {5 + 4*k*/ *k* ∈ *IN*}

$$\text{deg}(\mathbf{n}, \mathbf{N} = 3, \,\mathrm{D}\_{\ell}) = \left\{ \begin{array}{ll} \frac{n}{4} - \frac{3}{4}(2\ell + 1) + 1, \,\mathrm{if}\,\,\ell \text{ is odd} \\\ \frac{n}{4} - \frac{3}{4}(2\ell + 1) + \frac{1}{2}, \,\mathrm{if}\,\,\ell \text{ is even} \end{array} \right\} \tag{6}$$

D denotes the domain: <sup>1</sup> *<sup>n</sup>*+<sup>1</sup> <sup>2</sup> −- < *<sup>d</sup> <sup>C</sup>* <sup>≤</sup> <sup>1</sup> *<sup>n</sup>*−<sup>1</sup> <sup>2</sup> − where - ∈ 0, 1, 2, 3, . . . , *floor <sup>n</sup>*−<sup>9</sup> 6 + 1 .

In Appendix B, we represent the variation of domain degeneracy as a function of vaccination centre demands «site needs» for selected odd values of n. Furthermore, we plot in Figure 5, a generalization making possible to find the variation of such degeneracy for any odd number of vaccination centres.

**Figure 5.** A generalization making possible to find the variation of domain degeneracy for any odd number of vaccination centres.

(i) For n ∈ {6 + 4*k*/ *k* ∈ *IN*}

$$\deg\left(\mathbf{n}, \mathbf{N} = 3, \,\,\overline{D}\_{\ell}\right) = \left\{ \begin{array}{ll} \frac{n}{4} - \frac{3\ell}{2} + 1, \,\, if \,\,\ell \text{ is odd} \\\frac{n}{4} - \frac{(3\ell + 1)}{2} + 1, \,\,\, if \,\,\ell \text{ is even} \end{array} \right\} \tag{7}$$

*D* denotes the domain: <sup>1</sup> *<sup>n</sup>* <sup>2</sup> −-<sup>+</sup><sup>1</sup> <sup>&</sup>lt; *<sup>d</sup> <sup>C</sup>* <sup>≤</sup> <sup>1</sup> *n* <sup>2</sup> −where

$$\ell \in \left\{1, 2, 3, \ldots, floor\left(\frac{n}{6}\right)\right\} \tag{8}$$

(ii) For n ∈ {8 + 4*k*/ *k* ∈ *IN*}

$$\deg(\mathbf{n}, \mathbf{N} = 3, \ \mathbf{D}\_{\ell}) = \begin{cases} \frac{\text{II}}{4} - \frac{3\ell}{2} + 1, \text{ if } \ell \text{ is even} \\ \frac{\text{II}}{4} - \frac{(3\ell + 1)}{2} + 1, \text{ if } \ell \text{ is odd} \end{cases} \tag{9}$$

*D* denotes the domain: <sup>1</sup> *<sup>n</sup>* <sup>2</sup> −-<sup>+</sup><sup>1</sup> <sup>&</sup>lt; *<sup>d</sup> <sup>C</sup>* <sup>≤</sup> <sup>1</sup> *n* <sup>2</sup> − where - ∈ 1, 2, 3, . . . , *floor <sup>n</sup>* 6 .

In Appendix C, we represent the variation of domain degeneracy as a function of the vaccination centres demands for selected even values of n. Furthermore, we plot in Figure 6, a generalization making possible to find the variation of such degeneracy for any even number of vaccination centres.

**Figure 6.** *Cont.*

**Figure 6.** A generalization making possible to find the variation of domain degeneracy for any even number of vaccination centres.

As is observed in Appendices B and C and in Figures 5 and 6, these variations are represented by what we can call "descending ceiling functions".

In Figure 8, we reported the variation of the degrees of degeneracy deg(D0) and deg(*D*1). They correspond to the most degenerate domains for odd and even numbers of vaccination centres.

On the other hand, in Figure 7, we plot the variation of the degrees of degeneracy deg(Dp) and deg(*D*q) corresponding to the least degenerate domains for odd n and even n, respectively. They can be expressed by the following functions:

$$\deg(\mathcal{D}\_{\mathbb{P}}) = 1\\ \text{ord}\!\!g(\overline{\mathcal{D}}\_{\mathbb{Q}}) = 1, \text{ if } \mathbf{n} \in \{3k/k \in IN^{+}\} \cup \{5 + 3k/k \in IN\},$$

$$\deg(\mathcal{D}\_{\mathbb{P}}) = 2\\ \text{ord}\!g(\overline{\mathcal{D}}\_{\mathbb{Q}}) = 2, \text{ if } \mathbf{n} \in \{7 + 3k/k \in IN\},$$

$$\text{where } p = floor(\frac{n-9}{6}) + 1, \text{and } q = floor(\frac{n}{6}).$$

**Figure 7.** Variation of the degrees of degeneracy deg(Dp) and deg(*D*q) corresponding to the least degenerate domains.

**Figure 8.** Variation of degree of degeneracy deg(D0) and deg(*D*1) with n.

*5.3. General Expressions of the Number of Graphs (Different Paths) Using an Optimum Number N of Drones for Logistics Distribution*

Let us first note that for the trivially case, namely *<sup>d</sup> <sup>C</sup>* <sup>≤</sup> <sup>1</sup> *<sup>n</sup>* , delivery can be realized only by one drone. In this case, it is obvious that the drone has only one path to follow to accomplish the task, and therefore there exist only one graph which can be noted G{n, N = 1,(n)}, according to the adopted notation.

(a) General expressions of the number of graphs (paths) when the optimal number of drones is 2 (N = 2)

In the case N = 2 as optimum number of drones satisfying the maximum vaccination centres according to their demands, the corresponding domains and graphs are defined by the following intervals:


For *N* = 2, each domain *Di* or *Di* corresponds to one and only one graph. This means that the domains are not degenerated for any number n of vaccination centres and for any demands using necessary two drones. We have to note that, in this case and for a given zone with n centres, all graphs constructed for any domain have the same length *L*(n, N = 2). This later is given by:

$$L(\mathbf{n}, \mathbf{N} = 2) = (2\mathbf{n} - \mathbf{7}) \left[ 4 + 2(\mathbf{n} - 2)\sin\left(\frac{\pi}{\mathbf{n}}\right) \right] r. \tag{10}$$

Therefore, it does not depend on the topology of the graph and the vaccination centre demands when this later belongs to the ranges:


From the above ranges, we deduce that the total number *NG* (*n, N* = 2) of graphs, which correspond to N = 2 and for any number n of vaccination centres belonging to the same zone, is given by:

$$NG(\mathbf{n}, \mathbf{N} = 2) = \frac{n - 1}{2}, \text{for odd } \mathbf{n} \tag{11a}$$

$$NG(\mathbf{n}, \ N=2) = \frac{n}{2}, \text{for even } \mathbf{n} \tag{11b}$$

which is represented in Figure 9.

(b) General expressions of the number of graphs (paths) when the optimal number of drones is 3 (N = 3)

Let us first note that when we have to use three UAVs to deliver vaccines to vaccination centres belonging to same zone, all graphs constructed for any domain Di or *Di* have the same length which is given by:

$$L(\mathbf{n}, \mathbf{N} = 3) = (2\mathbf{n} - \mathbf{7}) \left[ 6 + 2(\mathbf{n} - 3) \sin\left(\frac{\pi}{\mathbf{n}}\right) \right] r. \tag{11c}$$

**Figure 9.** Dependence of the number of graphs *NG* (n, N = 2) as a function of n.

Thus, it does not depend on the structure of the graph. As demonstrated in Section 4.1, in order to satisfy the vaccination centres with N = 3 as optimum number of drones and according to our assumptions, the centre demands d have to belong to the following ranges:


So, the total number *NG* (n, N = 3) of graphs corresponding to N = 3 depends on the parity of the number n of vaccination centres. Thus,


$$NG(\mathbf{n}, \ N=3) = \sum\_{\ell=0}^{p} \deg(\mathbf{n}, \ N=3, \ D\_{\ell})$$

Using expressions Equations (4)–(6), we have demonstrated that *NG*(n, N *= 3)* also depends on the parity of *p*. Its expression is given by:

$$\begin{cases} \mathbf{n} \in \{2k + 1/k \in IN\} \\ flow(\frac{n-9}{6}) + 1, \text{ odd} \end{cases} \},$$

$$NG(\mathbf{n}, \mathcal{N} = 3) = \frac{1}{4} \Big[ flow\left(\frac{n-9}{6}\right) + 2\Big] \Big[ n - 3flow\left(\frac{n-9}{6}\right) - 3\Big]. \tag{12}$$

$$\begin{cases} \mathbf{n} \in \{3 + 4k \mid k \in IN\} \\ flow(\frac{n-9}{6}) + 1, \text{ even} \end{cases} \}$$

$$NG(\mathbf{n}, \mathcal{N} = 3) = \left[ flow\left(\frac{n-9}{6}\right) + 2\right] \left[ \frac{n}{4} + 1 \right] - \frac{1}{4} \Big[ flow\left(\frac{n-9}{6}\right) + 1 \Big] \Big[ 3flow\left(\frac{n-9}{6}\right) + 10 \Big] - \frac{3}{4}. \tag{13}$$

$$\begin{cases} \mathbf{n} \in \{5 + 4k \mid k \in IN\} \\ flow\left(\frac{n-9}{6}\right) + 1, \text{ even} \end{cases} \}$$

$$NG(\mathbf{n}, \mathcal{N} = 3) = \frac{1}{4} \left[floor\left(\frac{n-9}{6}\right) + 2\right] \left[n - 3floor\left(\frac{n-9}{6}\right) - 3\right] - \frac{1}{4}.\tag{14}$$

In Figure 10, we represent the evolution of the number of graphs *NG*(n, N = 3) in zones containing odd numbers of vaccination centres.

**Figure 10.** Dependence of the number of graphs *NG*(n, N = 3) as a function of odd n. *•*: (n ∈ {2*k* +1/ *k* ∈ *IN*}, odd p); **x**: (n ∈ {3+4*k*/ *k* ∈ *IN*}, even p); **\***: (n∈ {5+4*k*/*k* ∈ *IN*}, even p).


$$\text{NG}(\mathbf{n}, \mathbf{N} = \mathbf{3}) = \sum\_{\ell=1}^{q} \text{deg}(\mathbf{n}, \mathbf{N} = \mathbf{3}, \nabla\_{\ell})$$

Using Equations (7)–(9), we have demonstrated that *NG*(n, N = 3) also depends on the parity of q. Its expression is given by:

$$\begin{array}{l} \text{(iii)} \quad \left\{ \begin{array}{l} \mathbf{n} \in \{2k/\, k \in IN\} \\ flow(\frac{n}{6}) \text{ even} \end{array} \right\}, \\\\ \text{NG(n, N=3)} = \frac{n}{4} \left[ flow\left(\frac{n}{6}\right) \right] - \frac{1}{4} flow\left(\frac{n}{6}\right) \left[ 3flow\left(\frac{n}{6}\right) + 4 \right] + flow\left(\frac{n}{6}\right) \end{array} \text{(15)}$$
  $\text{(iv)} \quad \left\{ \begin{array}{l} \mathbf{n} \in \{6 + 4k/\, k \in IN\} \\ flow(\frac{n}{6}) \text{ odd} \end{array} \right\}\_{\mathbf{n}'}$ 

$$\begin{array}{l} \{\mathbf{v}\} \quad \left\{\begin{array}{l} \mathbf{n} \in \{6 + 4k/\ k \in IN\} \\ \hline \end{array} \right\}\_{\prime} \\\\ \mathrm{NG}(\mathbf{n}, \mathrm{N} = 3) = \frac{\mu}{4} \left[ \mathrm{floor}\left(\frac{\mu}{b}\right) \right] - \frac{1}{4} \left[ \mathrm{floor}\left(\frac{\mu}{b}\right) - 1 \right] \left[ 3\mathrm{floor}\left(\frac{\mu}{b}\right) + 1 \right] - \frac{1}{2} \mathrm{floor}\left(\frac{\mu}{b}\right) \end{array} \tag{16}$$

4

$$\begin{array}{ll} \text{(v)} & \begin{Bmatrix} \mathbf{n} \in \{8 + 4k/k \in IN\} \\ \end{Bmatrix} \\ \end{array}$$

$$NG(\mathbf{n}, \mathbf{N} = 3) = \frac{\boldsymbol{\mu}}{\mathbf{3}} \left[floor\left(\frac{\boldsymbol{\mu}}{\mathbf{5}}\right)\right] - \frac{1}{\mathbf{4}} \left[3floor\left(\frac{\boldsymbol{\mu}}{\mathbf{5}}\right) + 1\right] \left[floor\left(\frac{\boldsymbol{\mu}}{\mathbf{5}}\right) + 1\right] + floor\left(\frac{\boldsymbol{\mu}}{\mathbf{5}}\right) \tag{17}$$

6

6

6

In Figure 11, we plot the variation of the number of graphs *NG*(n, N = 3) in zones containing even numbers of vaccination centres.

4

,

**Figure 11.** Dependence of the number of graphs *NG*(n, N = 3) as a function of even n. *•*: (n ∈ {2*k*/ *k* ∈ *IN*}, even q); **x**: (n ∈ {6 + 4*k*/ *k* ∈ *IN*}, odd q); **\***: (n ∈ {8 + 4*k*/*k* ∈ *IN*}, odd q).

#### **6. Conclusions**

Over the last years, the use of drones is leading to new working models in a variety of logistic scenarios. This happens in both developed and developing countries. Currently, fascinating pilot and implementation projects, especially in Africa and Asia, reveal their true potential. By some predictions, the commercial drone market will triple by 2023.In healthcare section, the potential for drone use is vast, and hopefully drones are able to fill some niches where our performance needs improvement. Drones may significantly increase access to healthcare for individuals and large populations, particularly those who do not benefit from appropriate care due to remoteness and lack of infrastructure or funds. In this paper, we have proposed an exact analytical approach and operational strategy to the logistics of any pandemic vaccination effort. Using Unmanned Aerials vehicles (drones), our approach developed a procedure which can be used to deliver pandemic vaccines to densely populated cities or sparsely populate rural areas, whatever the number of population living there. Our strategy consists of dividing the concerned territorial area into zones in the form of circular bands. Each zone is divided into several isometric districts where each of them contains a vaccination centre. We have been interested in the route planning problem of the drones during the distribution. This latter concern the vaccines delivery from central depot to any number of vaccination centres. In the case of fixed and optimal number of the used drones, we have determined all equivalent and optimal flight path plans (graphs). This depends on the domain D of vaccination centre demand d. The existence of equivalent graphs, corresponding to a well-known domain d, incites us to define what we called "degeneracy of the domain Dd". The equivalent graphs (paths) have de same length, the same global cost and the same delivery time. It is worthy to note that, the existence of such degeneracy gives us the possibility to choose the most appropriate paths according to the emergency states of the vaccination centres. Then, using the notion, of degeneracy of the domain D for all domains, we have calculated the total number of graphs (paths) corresponding to the fixed and optimal number of the used drones. In our present investigation all relations has been expressed for any number of vaccination centres.

**Author Contributions:** Conceptualization, A.B, O.M., H.B. and N.B.; methodology, A.B., H.B. and N.B; investigation, A.B and H.B.; writing—original draft preparation, and co-wrote the manuscript, A.B., H.B. and N.B.; revised the manuscript and approved the final version, A.B, O.M., H.B. and N.B.; writing—review and editing, A.B. and N.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**

**Table A1.** Domains of d, corresponding graphs and lengths *L* (n, N) of the paths travelled by the set of optimum number of drones necessary for the logistics distribution, when zone contains n = 5, and 6 vaccination centres, respectively.


א א

א א

א א

**Figure A1.** The variation of optimum number N of drones as function of vaccination centre demands, for n = 5, and 6.

#### **Appendix B**

א א **<sup>n</sup>**א**} 3 + 4k/k** א**N},** *p* **= E(**ିૢ

**Figure A2.** *Cont.*

**Figure A2.** *Cont.*

**Figure A2.** *Cont.*

**Figure A2.** The variation of domain degeneracy as a function of vaccination centre demands «site needs» for selected odd values of n.

**Appendix C**

**For n fixe** א**} 8 + 4k/k** א**N},** *q* **= E(n/6)**

**Figure A3.** *Cont.*

**Figure A3.** The variation of domain degeneracy as a function of the vaccination centres demands for selected even values of n.

#### **References**


## *Article* **Numerical Calculation and Analysis of Water Dump Distribution Out of the Belly Tanks of Firefighting Helicopters**

**Tejun Zhou 1,2,\*, Jiazheng Lu 1, Chuanping Wu <sup>1</sup> and Shilong Lan <sup>3</sup>**


**Abstract:** Helicopters are more and more widely used for water dumping in fire extinguishing operations nowadays. Increasing attention is being paid to improving helicopter firefighting efficiency. Water distribution onto the ground from the helicopter tank is a key reference target to evaluate firefighting efficiency. Numerical simulations and calculations were carried out concerning water dumping out of the belly tank of a helicopter using the VOF (Volume of Fluent Model) model and mesh adaptation in ANSYS Fluent, and the effects of two parameters, the height of the tank above the ground and the wind speed, on the wake flow and water distribution were discussed. The results showed that for forward flight, the higher the forward flight speed, the less the average water depth on the ground. Similar results were obtained for flight height. The average water depth was one order of magnitude less than in the cases of the corresponding hovering helicopter for a given wind speed. As for hovering flight, the higher the wind speed, the less the average water depth on the ground. The simulation results were basically consistent with the conclusions of water dump tests of fire-fighting equipment carried by helicopters. For example, when the helicopter flew at a forward flight speed of 15 m/s and the tank bottom was 30 m above the ground, the area covered by the dumped water would be 337.5 m2, and the average water depth accumulated per square meter would be 0.3 cm. This result was close to the 0.34 cm obtained under Hayden Biggs's test condition with a forward flight speed of 70 km/h and a height above the ground of 24 m.

**Keywords:** helicopter; tank; water dump; wind speed; numerical calculation

#### **1. Introduction**

Forests in China cover an area of nearly two million square kilometers, accounting for nearly 20% of the country's land area. Forest fires occur frequently every year, causing extensive damage to natural resources, the ecological environment, and production facilities [1–3], and even sometimes causing heavy casualties. Therefore, it is very important to carry out proper monitoring, early warning, and forest fire suppression. During forest fire suppression, helicopters can rapidly reach the forest, where it is difficult for people to enter to extinguish the fire. The suppression achieved by the helicopter's water dumping on the fire line and the fire head reduces the intensity of effort by ground personnel against the fire and reduces the casualty rate. At present, firefighting departments in the United States, Canada, Russia, Japan, and other countries are equipped with many firefighting helicopters to execute tasks such as forest fire suppression and high-rise building firefighting [4,5]. Because the aviation industry in China started late, it has lagged behind the developed countries just mentioned in both research and development and the quantity of firefighting helicopters. Moreover, technology and applications related to helicopter firefighting are also in need of development. Helicopter firefighting mainly includes onboard tank

**Citation:** Zhou, T.; Lu, J.; Wu, C.; Lan, S. Numerical Calculation and Analysis of Water Dump Distribution Out of the Belly Tanks of Firefighting Helicopters. *Safety* **2022**, *8*, 69. https://doi.org/10.3390/ safety8040069

Academic Editor: Raphael Grzebieta

Received: 25 February 2022 Accepted: 28 May 2022 Published: 3 October 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

(belly/under-deck) water dumping, bucket/capsule water dump firefighting, fire watermonitor firefighting, and fire water-bomb drop firefighting. The firefighting effect is closely related to the water distribution in the target region [6,7]. Studies on water distribution in onboard tanks and bucket/capsule water dump firefighting mainly came from flight tests. The following is a review of studies on water distribution in onboard tank firefighting and bucket /capsule water dump firefighting [8–15].

Experimental data from the studies just described are as follows, where the water depth accumulated was an average, whereas the data from Xie Yingmin et al. [12] were merely the results on flat ground. The results of Wu Zepeng et al. [8] show that if the bucket was more than 30 m above the fire scene, the water dumped would be atomized completely, whereas the results of both Xie Yingmin et al. [12] and Zhou Tejun et al. [13] showed that, at a height of 30 m, the water depth accumulated was still 0.1–0.2 cm. The results of Chen Zhaopeng et al. [10] and Zhou Wanshu [11] showed that at a height of 50 m, the water depth accumulated could reach 0.2 cm, and could even reach 1.25 cm under the no-wind circumstance, as proved by Chen Zhaopeng et al. [10]. These results were obviously inconsistent with each other. Such an inconsistency might have been due to several aspects, for example, whether foaming agent and other surface-active materials had been added to the water. If so, the materials could reduce the formation of small water droplets. In addition, the bucket bottom valves might have been of different sizes and shapes, which would have an impact on water flow and pattern, thus resulting in differences in water dump coverage areas and the average water depth on the ground.

Because renting helicopters is expensive, the firefighting tests involve both great material consumption and high cost, and fine data cannot be obtained through conventional test techniques. Therefore, the helicopter firefighting test is restricted; however, as one of the study objectives, numerical simulation can either supplement or even replace such tests. With current physical firefighting process knowledge of water dumping out of helicopters, the application of relevant models, and constant development of numerical simulation software and computer performance, numerical simulation of firefighting by water dumping out of helicopters has developed gradually from nothing. However, its technical level has not yet reached maturity, and there are few simulation studies of firefighting by water dumping out of helicopters. Two such studies will be briefly introduced in the following.

In the calculation model of X. Zhao et al. [16], the fact or principle used to set the diameter of the water droplets was not specified, nor were the calculation results verified by experiment. If the distribution rule of water droplet diameters were known beforehand, the calculation scheme of X. Zhao et al. would be feasible. In the study of Satoh et al. [17], the actual rotor wings of the helicopter were not simulated in the numerical simulation, and the downwash velocity field generated from the rotor wings was approximated by setting a downward air velocity of 30 m/s at the upper boundary of the computational domain, an approach that greatly reduced computational effort. Borisov et al. [18] performed a relatively complete study on water dump firefighting simulation. The blades were not simulated; instead, a downward speed was imparted to the plane of the lower blade by means of a virtual blade, in accordance with the measured velocity distribution, and a corresponding velocity was imparted to the plane of the upper blade.

The above discussion confirms that when a model with low degree of approximation was used to simulate a tank or bucket water dump process, a relatively accurate water distribution was not provided, and the accuracy of firefighting effect evaluation was affected. In addition, regarding the influence of the height of the tank or bucket above the ground on water distribution over the ground, there were also inconsistent conclusions in these articles. Evaluation of firefighting effect can be expressed by the water volume arriving at the ground fire source, where height above the ground is an important parameter influencing ground water distribution. In addition, because natural wind speed is hard to control, there were few reports in the literature concerning the influence of wind speed on water distribution.

#### **2. Helicopter and Tank Models**

In the present paper, simulation calculation of helicopter tank water dumping was performed using two parameters: the height of the helicopter tank bottom above the ground and the wind speed. The volume-of-fluid model (VOF model) was used to calculate the air-water interface, and dynamic mesh adaptation was used to better differentiate the air-water interface. The rule of influence of the height of the helicopter tank bottom above the ground (*H* = 10 m, 20 m, and 30 m) and the wind speed (*U* = 0 m/s, 5 m/s, 10 m/s, and 15 m/s) on the distribution of a water dump was given to provide theoretical guidance for a helicopter firefighting operation scheme. In this approach, to calculate the rotor wake, the acting disc theory of a helicopter was used instead of a simulated blade. This was more convenient to use than the virtual screw disk of Borisov et al. [18], which yields basically the same accuracy, and was more accurate than the jet model of Satoh et al. [17]. To calculate the water dump, this paper simulated the water discharge process of real water tank directly, while Satoh et al. [17] and Borisov et al. [18] did not simulate the water dump process. For the two-phase, water–air flow, this paper adopted the volume-fraction model for calculations, which is superior to the virtual gas model of Satoh et al. [17]. However, as this model is restricted by the extremely numerous calculations required, we did not calculate the breakup of drops; we note that the drops calculated by Borisov et al. [18] were also not real fluid drops, but water drop test particles representing many fluid drops.

An H125 helicopter equipped with an Isolair Eliminator II belly firefighting tank (https://www.fs.fed.us/t-d/pubs/html/95571307/95571307.html, accessed on 2 May 2022) was taken as the simulation prototype in this paper. Figure 1 shows a water dump out of an H125 helicopter equipped with the Isolair Eliminator II belly firefighting tank. Modeling was performed in accordance with the geometrical parameters of the H125 helicopter and the tank (ANSYS Design Modeler), neglecting some parts and configuration details such as the aero-engine case, the bracket under the fuselage, and the tail rotor. In this way, the helicopter and tank models used for simulation were obtained, as shown in Figure 2. The action of the blade on air was viewed as a pressure difference acting above and below a disc, specifically the *Fan* model in Fluent, which was more accurate than the jet flow approximation used by Satoh et al. [17]. If the geometrical parameters and operating parameters of the blade were known, the momentum source method [19] could also have been used to simulate the action of the blade on air, which would have been more accurate than the acting disc theory, and there is also a momentum source model in Fluent. Both the *Fan* model and the momentum source model eliminate the large numbers of mesh cells required to simulate actual blades, while still obtaining a relatively accurate time-mean wake flow field.

**Figure 1.** H125 firefighting helicopter and Isolair Eliminator II belly firefighting tank (from http://www. isolairinc.com/\_gallery/4600-350A.jpg, accessed on 2 May 2022).

**Figure 2.** Helicopter and tank model in the simulation.

The tank used in the calculation was 2.32 m long, 1.38 m wide, and 0.4 m high, with two long narrow valves, each 2 m long and 0.23 m wide with a gap of 0.3 m. The tank had a maximum capacity of 1280.64 L. To maintain consistent air pressure inside and outside the tank at the time of water dumping, a long narrow ventilation opening was designed over the rear of the tank (see Figure 3) with dimensions of 1.38 m × 0.05 m.

**Figure 3.** Details of the tank model (A is the water-dump valve, and B is the ventilation opening, for the dimensions of the tank and valve, see the description given in the main text).

#### **3. Water Dump Simulation Model of Helicopter Belly Firefighting Tank**

A parametric study was carried out in this paper regarding two key parameters that influence the distribution of the water dump: the height (H) from the tank bottom to the ground and the wind speed (U). Several examples for different heights (*H* = 10 m, 20 m, and 30 m) and wind speeds (*U* = 0 m/s, 5 m/s, 10 m/s, and 15 m/s) were calculated. The results of a calculated example are given in detail below (the height (*H*) from the tank bottom to the ground = 20 m, and the headwind speed *U* = 15 m/s), including mesh independence verification, the calculation format, and calculation scheme. This example was selected for a detailed analysis for the reason that, in this example, the height was moderate while the wind speed was relatively big, which caused very significant changes in the trajectory and shape of the water masses. Other calculated examples are given in Section 4, where the results of different heights above the ground and different wind speeds were investigated, and the rule of water distribution on the ground was generalized.

When the helicopter flew above the fire scene to prepare for a water dump, the airflow was generally stable surrounding the helicopter (the fire scene model was temporarily left out of consideration in this study). Therefore, before the water dump is calculated, the stable airflow field should be calculated first. This was then taken as the initial scenario to start transient calculations of the water dump.

#### *3.1. Mesh Independence Verification*

This section discusses the influence of mesh cell size on flow field results and especially on the resolution of the water–air phase interface. Two sets of meshes were used; namely, one set consisting of a basic mesh, and another with a fine grid. The verification was divided in two steps, where the first step compared the calculation results of the rotor flow field before water dump in the two sets of meshes, and the second step compared the calculation results of the two-phase, water–air flow after water dump in the two sets of meshes.

Figure 4 shows the simulation field of the helicopter dumping firefighting water. The blade disc diameter of the H125 helicopter (D) was 10.69 m, the distance from the front of the disc to the entry plane of the computational domain was 6D, the distance from the rear of the disc to the exit plane of the computational domain was 8D, the distance from the disc to both boundaries of the computational domain was 6D, and the distance from the disc to the upper boundary of the computational domain was 7D.

**Figure 4.** Computational domain of the helicopter.

For example, when the tank was 20 m from the ground, meshes generated by ANSYS Meshing, there were a total of 695,114 mesh cells (tetrahedrons and triangular prisms). The maximum mesh cell size inside and outside the tank was 0.05 m, the maximum size on the fuselage and on the disc of the rotor wings was 0.1 m, the maximum size on the external boundary plane of the computational domain was 5 m, and there were boundary-layer meshes (triangular-prism cells) on the disc of the rotor wings, the fuselage surface, the tank wall surface, and the ground. The thickness of the boundary layer was set to 0.05 m, there were 10 layers of mesh cells inside the boundary layer, and the mesh growth rate was 1.2; this mesh is referred to as the basic mesh in what follows. In Figure 5, the meshes near the helicopter and the tank on the longitudinal symmetry plan of the computational domain are given; the mesh cells in the tank can also be seen.

**Figure 5.** Meshes near the helicopter and tank on a longitudinal symmetric plan of the computational domain (there are boundary-layer meshes on the fuselage surface, the external tank surface, and both sides of the blade disc).

These new mesh cells are hereinafter referred to as fine meshes. They covered the spatial region from the bottom of the helicopter belly firefighting tank to the ground, which was 6.7 m long, 7 m wide, and 20 m high (as shown in the left side of Figure 6, the "body of influence" in ANSYS Workbench meshing was used), the maximum mesh cell size was set to 0.2 m. There were a total of 2,061,091 mesh cells, about three times the number (695,114) in the basic mesh cells described earlier. As will be seen later, the total number of mesh cells calculated up to 1.9 s reached 2,460,231 due to adaptive refinement of meshes.

**Figure 6.** Fine mesh space region and mesh distribution.

The calculation method, format parameters, and self-adaptive mesh parameters were all set the same in the two sets of meshes. Results from the fine meshes are given below and are compared with the results of the basic meshes. Figure 7 shows the pressure distribution on the longitudinal symmetry cross section of the initial scenario as calculated with fine meshes. There was almost no difference compared with the results of the basic mesh. In fact, the place where mesh refinement was performed was the space below the helicopter belly, and compared with the pressure gradients near the helicopter rotor wings and near the fuselage surface, the pressure gradient in this space was relatively gentle, and the basic meshes were sufficient to calculate the pressure field accurately.

**Figure 7.** Pressure distributions on a longitudinal symmetry cross section of the initial scenario calculated with fine meshes (the ground is at the ruler in the figure, the left picture is the basic mesh, and the right picture is the fine mesh).

Next, we compared the calculation results of two-phase, gas–fluid flow in the two sets of meshes. Figure 8 gives contour surface diagrams for water–air phase volume fractions of 0.01, 0.1, and 0.5 calculated with fine meshes at *t* = 1.9 s (i.e., the water mass touched the ground just at this time). It is obvious that the fine mesh could yield a finer water–air interface and smaller water mass, but the physical quantity of interest in this paper is the average water depth (i.e., the average water depth that is equal to the result of water-dump quantity divided by the water coverage area). The longitudinal and transverse dimensions of the water mass near the ground in Figure 8 were about 3 m × 4 m, and the calculation result of the base grid was about 4 m × 7 m, which shows that a more accurate water distribution could be obtained using the basic meshes. In Section 4.4 below, the average water depth accumulated as calculated in this paper was basically consistent with that under the corresponding condition by Xie Yingmin et al. [12], which showed that it was suitable to use the basic meshes to calculate the region covered by water and the average water depth. In addition, a third finer mesh was not taken into consideration in this paper since the calculation quantity of the fine mesh was sufficient.

**Figure 8.** Contour surface of the side view and front view for a two-phase, water–air volume fraction of 0.01 at *t* = 1.9 s.

#### *3.2. Analysis of Initial Scenario Results before Water Dump*

This section first gives the calculation results of the initial flow field before the water dump. VOF can be either enabled or disabled at the time of initial scenario calculation, and VOF was disabled in this study. The internal space of the tank was set to air, and the valves and the ventilation opening were set as solid wall surfaces. The calculation was performed by a steady-state algorithm, using the k-omega SST turbulence model [20]. Since complex separation only existed near the helicopter and water tank, the wake flow with which we were concerned under the water tank was not so complexed, and to which common turbulence models were applied; hence, the equation calculation format was SIMPLE, and basic meshes were used.

Figure 9 shows the calculated residual change curve. When the number of iterations was greater than 200, the residue remained basically unchanged. The velocity field (Figure 10) and the pressure field (Figure 11) on the longitudinal symmetry plane of the fuselage at 1000 and 2000 iterations were taken, respectively, as their simulated values, and the pressure shown in Figure 11 was gauge pressure. The velocity and pressure fields at 1000 and 2000 iterations were very consistent, showing that the calculation had reached steady state. Flow field data at 2000 iterations were selected as the initial scenario for subsequent calculations of the water dump.

**Figure 10.** Velocity vector on the longitudinal symmetry plane of the fuselage in the initial scenario (1000 iterations on the (**left**), 2000 iterations on the (**right**)).

**Figure 11.** Pressure distribution on the longitudinal symmetry plane of the fuselage in the initial scenario (1000 iterations on the (**left**), 2000 iterations on the (**right**)).

#### *3.3. Transient Result Analysis of Water Dump*

When the transient calculations of the water dump were enabled, steady-state (1600 iterations) data were read in, and the valves and ventilation opening were set as internal boundaries. Most of the space inside the tank, 2.32 m × 1.38 m × 0.35 m (length × width × height), was defined as a region called *Region0* using cell registers in Fluent, and the initial value of this region was adjusted by *Patch* when Fluent was initialized. Specifically, the phase in this region was adjusted to water, and therefore there was initially 1.12 m3 of water in the tank. Note that there was still air inside the tank at a height of 0.35–0.4 m, which connected with the air outside the tank through the ventilation opening. Data for other spaces required no

initialization and were maintained at the input steady-state values. The turbulence model and the spatial calculation format were kept the same as for the steady-state calculation.

Time was advanced by a first-order implicit method with a fixed time step of 0.001 s, corresponding to the rapidest water mass movement at approximately 1–2 cm. This ensured that there was sufficient time resolution, and the maximum number of iterations per time step was set to 50, so as to ensure residuals below 10<sup>−</sup>5. Transient calculation was enabled to *t* = 0.01 s, and the residual change was as shown in Figure 12. It is apparent that the residuals were significantly reduced by two or three orders of magnitude after bridging the transient calculation. If the transient calculations were continued, the residual of each equation could be maintained at 10−<sup>5</sup> to 10−<sup>6</sup> until the calculation ended at 1–2 s (as was the case with all transient calculation examples in this paper). When *t* = 0.01 s, the VOF distribution of water and air inside the tank and at the valve was as shown in Figure 13. If a cross section were taken in the middle of the tank vertical to the x-axis, meshes inside and below the tank could be seen (Figure 14), there were some flat triangular cells, which were formed by cutting off tetrahedral cells in cross section, and most of the mesh cells were near-regular tetrahedra (Figure 5).

**Figure 12.** Residual change curve of steady-state calculations bridging to transient calculations (until *t* = 0.02 s).

**Figure 13.** VOF distribution of water and air inside the tank (**left**) and at two values at the tank bottom (**right**) when *t* = 0.01 s (red indicates water).

Dynamic mesh adaptation (based on the curvature of the water–air interface) was enabled after the tank water dump had been enabled for 0.01 s. Meanwhile, mesh adaptation was set at one per time step, with the time step still being 0.001 s, and for each time step, mesh adaptation, the coarsening threshold (10−8) and the refining threshold (10−2) were implemented. In addition, dynamic self-adaptation was enabled, the maximum level of refinement was set to 2, the minimum cell volume was set to 1.25 × <sup>10</sup>−<sup>4</sup> m3 (the corresponding mesh cell was 0.05 m), and mesh adaptation load balancing was used to improve parallel efficiency. The calculation lasted from *t* = 0.01 s to *t* = 0.45 s. The VOF distribution and the meshes of water and air on the same cross section are shown in Figure 12. The meshes near the water–air interface were encrypted to a certain extent so that the water–air interface could be better distinguished.

**Figure 14.** Mesh distributions inside and below the tank in cross section.

Figure 15 shows the water in the tank and nearby meshes at *t* = 1.9 s of the water dump. At this time, most of the water in the tank has been dumped. Figure 8 shows the contour surface with a water–air volume fraction = 0.01 in space (the ground is at the ruler in the figure). The side view in Figure 8 shows that large water masses have been subjected to a certain influence by Level-3 wind, the dumped water has been deflected in the wind direction, the water mass near the ground has been deflected in the wind direction by 3–4 m, and the longitudinal dimension of the water mass has reached about 4 m. The front view in Figure 8 shows that under the action of wind, the water flow has developed laterally, and that the sideways deflection of the water mass near the ground is about 7 m. This means that the area covered by the water dump on the ground is approximately 4 m × 7 m = 28 m2, under the assumption that all 1.12 m<sup>3</sup> of the water in the tank was dumped to this region. The average water depth accumulated in this region would then be approximately 0.04 m. Although in fact small water droplets would be created and would fly away with the wind, thus causing the region covered by water to be larger than the value calculated above, in the dense mesh calculation (Figure 8), the area covered by the water dump on the ground was approximately 3 m × 4 m = 12 m2. Therefore, taking the two circumstances causing contrary results into full consideration, the region covered by water might not have been underestimated in the calculation using basic meshes. Hence, the region covered by water and the average water depth accumulated from the above basic mesh calculations were used as important data for drawing conclusions.

**Figure 15.** VOF distribution and network of water and air on the cross section inside and under the tank (*t* = 0.45 s and *t* = 1.9 s).

Comparing the side view in Figure 16 with the water dump picture in Figure 17 reveals a similar important phenomenon: the water flow was not smooth or continuous, but experienced many interruptions. Only a rough qualitative comparison could be performed because the forward flight speed of the helicopter in the picture and the wind speed were unknown. Except for the fact that small water droplets could not be differentiated in the calculations, the water masses were of similar qualitative distribution, showing that the calculated results were qualitatively correct. Figure 18 gives a local panoramic view of the two-phase, water–air volume fraction contour surface below the helicopter belly at two moments, *t* = 0.9 s and *t* = 1.9 s. The water–air interface at *t* = 0.9 s was relatively more continuous than that at *t* = 1.9 s, because the water dump flow was greater at the former. These images resemble the photograph of the helicopter belly firefighting tank water dump in Figure 1. Because of the lack of quantitative experimental data in the literature, the results calculated here were only qualitatively compared with the actual pictures.

**Figure 16.** Panoramic view of the contour surface for a volume fraction = 0.01 in space at *t* = 1.9 s (the side and front views are shown in Figure 8).

**Figure 17.** AS350B2 firefighting tank used for water dump firefighting (found online at http://www. isolairinc.com/\_gallery/4600-350D.jpg, accessed on 2 September 2021).

**Figure 18.** Local panorama of contour surface when the volume fraction of the water–air phase below the helicopter belly was 0.01 ((**left**), *t* = 0.9 s; (**right**), *t* = 1.9 s).

In fact, it is very difficult to simulate the movement of real water masses and water drops after water dump, regarding which a discussion is made below. The main force on the water mass by the airflow was in direct proportion to ρair*U*2*D*2, and the force of gravity on the water mass was in direct proportion to ρwater*D*3g, where *D* was the equivalent diameter of the water mass, *U* was the velocity of the water mass relative to the airflow, and g was the acceleration of gravity. When the force exerted on the water mass by the airflow was comparable to that of gravity, the water mass could significantly move along with the airflow. However, it can be inferred that only water droplets with diameter less than 1 cm could move significantly with the airflow, and the smaller the water droplets, the more closely they moved with the airflow. In our calculations, the minimum mesh cell scale was about 0.05 m, and it was impossible to distinguish water droplets less than 0.01 m in diameter. The equivalent diameters of the water masses of VOF-to-DPM [21] conversion in ANSYS Fluent were set to 0.01 m; therefore, the conversion was not activated. If a smaller mesh cell size and a smaller equivalent diameter of VOF-to-DPM water mass were adopted, the movement of small water droplets with the airflow could be calculated.

Interruption of the water–air interface occurred because of instability on the interface between the falling water flow and the air at greater Weber number. The interface then formed a complex curved surface, which was then broken into large water droplets, which would also experience instability with the air interface, leading to secondary breakage and creating still smaller water droplets. The water distribution of the water dump out of the helicopter involved a distance of dozens of meters from the tank to the ground and the passage of several seconds. The instability and breaking of the water flow and the secondary breakage of large water droplets occurred at a smaller space and time scale [22–25], which was nearly impossible to consider simultaneously in the simulation calculations. A water droplet breakage model would generally be used (many breakage models are available in ANSYS Fluent).

If sufficient calculation resources can be obtained, the mesh should be finer as much as possible, which can make the simulation of the water–air interface finer, and, if possible, one should adopt the breaking-drop model. A further analysis of the calculation results produced by the fine mesh is provided below. Figure 19 gives contour surface diagrams when the water–air phase volume fraction calculated with fine meshes at *t* = 1.9 s was 0.01, 0.1, and 0.5. The three contour surfaces were of relatively similar form, showing that the two-phase, water–air interface was reconstructed with reasonable accuracy under this fine mesh and with the mesh adaptation calculations. Figure 20 shows a local enlargement of the results near the ground in Figure 19, with the contour surface with volume fractions of 0.01 and 0.5, and in addition shows the mesh cells at that location on the contour surface. The maximum mesh cell size of the refined meshes near the ground was 0.2 m, and the

minimum cell size of the mesh adaptation was 0.05 m. Therefore, the maximum mesh cell size was 0.05 m, which meant that water droplets smaller than 0.05 m could not be distinguished. Due to insufficient mesh refinement in the present calculations, the "VOF-to-DPM" model in ANSYS Fluent was not activated, and therefore the water droplet breakage model was not used.

**Figure 19.** Contour surface of the two-phase, water–air volume fraction with fine meshes (the ground is at the ruler). (**a**) Contour surface and side view when the two-phase, water–air volume fraction was 0.01, 0.1, and 0.5, respectively, at *t* = 1.9 s. (**b**) Contour surface and front view when the two-phase, water–air volume fraction was 0.01, 0.1, and 0.5, respectively, at *t* = 1.9 s.

(**b**)

**Figure 20.** Contour surface of volume fraction near the ground and mesh cells in this region (the volume fraction was 0.01 in the (**left**) figure and 0.5 in the (**right**) figure).

It was calculated in the above example that, at *t* = 1.9 s, the water was close to the ground. If the calculation had continued, it would quickly have become unstable, because in the very short time when the water masses or large droplets hit the ground, the water mass is deformed and broken, and bouncing motions and other complex deformation and motion phenomena occur. The current mesh cell size and time step cannot distinguish such rapid and drastic changes, leading to instability in the calculations. Assuming that the main flow characteristics and the water–air distribution were obtained when the water was close to the ground, and assuming that the water in the air fell to the ground according to its existing trajectory for the rest of its time airborne, the case that the water continued to fall to the ground was not considered in this paper. If the complex process of water hitting the ground is ignored and the ground is considered as a porous media model that allows only water to pass through, or if the ground is set as a pressure outlet boundary, the problem of unstable calculations can be avoided, and an approximate distribution of accumulated water on the ground can be obtained.

#### **4. Simulation Conclusion Analysis and Rule of Water Dumping Out of Helicopter Belly Firefighting Tank**

To provide theoretical guidance for helicopter firefighting practices, a study on parameters influencing the water dump distribution was performed in this section regarding two key parameters: the height of the tank bottom above the ground (*H*) and the wind speed (*U*). A total of 12 calculation examples were considered, with *H* = 10 m, 20 m, and 30 m, and *U* = 0 m/s, 5 m/s (Level 3), 10 m/s (Level 5), and 15 m/s (Level 7). The wind direction pointed to the rear of the helicopter, or in other words, the helicopter flew into the wind. The settings of the basic meshes, computational domain, mesh dissolution, and the calculation model and method in this section were the same as those used in the examples in Section 3.

#### *4.1. Result Analysis and Summary of Initial Scenario before Water Dump*

The influence of the height of the helicopter tank bottom above the ground and of wind speed on the distribution scope of wake flow was analyzed and is summarized as follows. Figure 21 shows the distribution of wake flow when the helicopter tank bottom was 10 m above the ground and the wind speed was 0 m/s, 5 m/s, 10 m/s, and 15 m/s. Figure 22 shows the distribution of wake flow when the helicopter tank bottom was 20 m above the ground, for the same values of wind speed. Figure 23 shows the distribution of wake flow when the helicopter tank bottom was 30 m above the ground, for the same values of wind speed. These figures show that wind speed had a very significant influence on the wake flow direction of the helicopter, and when the height above the ground was between 10 and 30 m, the wake flow could be deviated by nearly 30 degrees from the

straight rearward direction (the wind direction) by a wind speed of 5 m/s. The deviation increased to around 45 degrees at a wind speed of 10 m/s and around 60 degrees at a wind speed of 15 m/s. Wake flow was also influenced by the height above the ground: the higher the helicopter was above the ground, the lower the wake flow speed near the ground. When the helicopter hovered in a wind at 30 m/s, the wake flow speed near the ground was around 8 m/s. The ground in Figures 21–23 is near the ruler.

**Figure 21.** Distribution of wake flow when the helicopter tank bottom was 10 m above the ground (wind speed was 0 m/s, 5 m/s, 10 m/s, and 15 m/s; reference speed marked on the fuselage, indicated by a blue arrow, and the reference speed is 30 m/s).

**Figure 22.** Distribution of wake flow when the helicopter tank bottom was 20 m above the ground (wind speed was 0 m/s, 5 m/s, 10 m/s, and 15 m/s; reference speed marked on the fuselage, indicated by a blue arrow, and the reference speed is 30 m/s).

**Figure 23.** Distribution of wake flow when the helicopter tank bottom was 30 m above the ground (wind speed was 0 m/s, 5 m/s, 10 m/s, and 15 m/s; reference speed marked on the fuselage, indicated by a blue arrow, and the reference speed is 30 m/s).

#### *4.2. Transient Result Analysis and Summary of Water Dump*

Figure 24 shows the contour surface of the two-phase, water–air interface at a volume fraction of 0.01 when the helicopter tank bottom was 10 m above the ground and the wind speed was 0 m/s, 5 m/s, 10 m/s, and 15 m/s (*t* = 1.2 s, when the water mass was close to the ground). The figure shows that the motion trajectory of large water masses was basically not influenced at a wind speed of 5–10 m/s when the helicopter was 10 m above the ground, but at a wind speed of 15 m/s, the water masses moved slightly in the wind direction. The front view reveals that the water masses expanded significantly in the horizontal direction, with a horizontal expansion of nearly 50% compared with their size at a wind speed of 0 m/s.

Figure 25 shows the contour surface of the two-phase, water–air interface at a volume fraction of 0.01 when the helicopter tank bottom was 20 m above the ground and the wind speed was 0 m/s, 5 m/s, 10 m/s, and 15 m/s (*t* = 1.8 s, when the water mass was almost reaching the ground). Large water masses were basically not influenced at a wind speed of 5–10 m/s, but when the wind speed was 15 m/s, the water masses deviated significantly in the wind direction, with a deviation of 2–3 m compared with that at a wind speed of 0 m/s. The front view shows that the water masses also expanded significantly in the horizontal direction, with a horizontal expansion of around 7 m, which was around three times its horizontal extent at a wind speed of 0 m/s.

**Figure 24.** Contour surface of the two-phase, water–air interface at a volume fraction of 0.01 under different wind speeds (*H* = 10 m; the ground is at the ruler in the figure; *t* = 1.2 s). (**a**) Side view, showing *U* = 0 m/s, 5 m/s, 10 m/s, and 15 m/s, respectively, from left to right. (**b**) Front view, displaying *U* = 0 m/s, 5 m/s, 10 m/s, and 15 m/s, respectively, from left to right.

**Figure 25.** Contour surface of the two-phase, water–air interface at a volume fraction of 0.01 under different wind speeds (*H* = 20 m; the ground is at the ruler in the figure; *t* = 1.8 s). (**a**) Side view, displaying *U* = 0 m/s, 5 m/s, 10 m/s, and 15 m/s, respectively, from left to right. (**b**) Front view, showing *U* = 0 m/s, 5 m/s, 10 m/s, and 15 m/s, respectively, from left to right.

Figure 26 shows the contour surface of the two-phase, water–air interface at a volume fraction of 0.01 when the helicopter tank bottom was 30 m above the ground and the wind speed was 0 m/s, 5 m/s, 10 m/s, and 15 m/s, at around *t* = 2 s. In a similar manner, at a wind speed of 15 m/s, the water masses deviated significantly in the wind direction, and the water masses also expanded significantly in the horizontal direction, reaching around 9 m.

**Figure 26.** Contour surface of the two-phase, water–air interface at a volume fraction of 0.01 under different wind speeds (*H* = 30 m; the ground is at the ruler in the figure; *t* = 2.1 s). (**a**) Front view, showing *U* = 0 m/s, 5 m/s, 10 m/s, and 15 m/s, respectively, from left to right. (**b**) Front view, portraying *U* = 0 m/s, 5 m/s, 10 m/s, and 15 m/s, respectively, from left to right.

These observations inform us that wind speed had a very significant influence on the helicopter wake flow direction. When the height above the ground was 10–30 m, the wake flow could be deviated for nearly 30 degrees from the straight rearward direction (the wind direction) when the wind speed was 5 m/s. The deviation was around 45 degrees at a wind speed of 10 m/s and around 60 degrees at a wind speed of 15 m/s. The wake flow was also influenced by the height above the ground; the higher the helicopter, the lower the wake flow speed near the ground, and when the helicopter hovered at 30 m/s, the wake flow speed near the ground was around 8 m/s.

Large water masses were basically not influenced at wind speeds of 5–10 m/s, but when the wind speed was 15 m/s, the water masses deviated significantly in the wind direction and expanded significantly in the horizontal direction. The higher the water dump tank was above the ground, the greater the influence of wind speed on the water mass distribution.

#### *4.3. Forward Helicopter Flight*

In Section 4, it was assumed that the helicopter was hovering. In fact, before firefighting, the helicopter may fly forward at low speed above the targeted fire scene. For example, in the case where the forward flight speed was 10 m/s and there was no wind in the horizontal direction, this state could be approximated by the helicopter hovering in accordance with the principle of relativity of motion, with a headwind of 10 m/s. In addition, changes in the dip angle of the rotor discs were neglected in the calculation model. Regarding the problem of water dump distribution, although only the height of the helicopter tank above the ground and the wind speed were discussed in Section 4, the calculated result could be approximated by the circumstance where the helicopter was flying at a corresponding forward flight speed. The difference in the approximation came from changes in the dip angle of the rotor discs and the ground boundary layer, both of which had a small influence. Of course, if the hot air at the fire scene itself were taken into consideration, both wind speed and wind direction would have a significant influence on the hot air, and therefore the principle of relativity of motion might not be applicable. In the following discussion, the results obtained in Section 4 were applied to the circumstance of forward helicopter flight in accordance with the principle of relativity of motion.

Assuming that the helicopter tank was 20 m above the ground, the helicopter flew forward at a speed of 15 m/s (i.e., 54 km/h) and there was no wind (Figure 27b), then this would be equivalent to the case where the helicopter hovered against the wind at 15 m/s and the ground moved at 15 m/s in the wind direction (Figure 27a). Figure 27a shows that the helicopter hovered initially right above Point O on the ground, and when the headwind was 15 m/s, the water masses reached Point P on the ground at about 1.8 s, with a deviation of about 2–3 m from the wind direction. At this time, the water in the tank had run out, and most of the water dumped into the air would have fallen to the ground in approximately 1.8 s. Assuming that the ground moved leftward at a speed of 15 m/s, water fell finally at Point Q on the ground, and PQ was the region covered by most of the water, with an approximate length of 15 × 1.8 = 27 m. At this time, Point O had moved to Point O .

Figure 27b shows that if the helicopter flew forward at a speed of 15 m/s, there was no wind, the ground was fixed, and initially the helicopter was right above Point O' on the ground, it flew to be right above Point O on the ground 1.8 s later, the water dumped initially fell to Point P on the ground at this time. Similarly, around 1.8 s later, most of the water would have fallen, finally reaching Point Q on the ground. In this case, the PQ region was the region covered by most of the water, with an approximate length of 15 × 2 = 30 m. Figure 25 shows that the horizontal width of the region was around 7 m, the region covered an area of about 30 × 7 = 210 m2, and after 1.12 m3 of water were dumped, there would be about 5 mm of water accumulated per square meter in the covered region.

Figure 27b shows that if the intent is to dump water in the right region starting from Point P on the ground (PQ), the pilot needs to open the tank valve to dump the water when the helicopter is right above Point O'. The region covered by the water dumped depends on the height of the tank bottom above the ground, the flight speed, the wind speed, and the time required to empty the tank.

Note that in these calculations, foaming agents and other surface-active materials were not added to the water. If surface-active materials were added, formation of water droplets and the vaporization speed of water could be reduced, thus reducing the area covered by water on the ground and increasing the amount of water distributed per unit area.

**Figure 27.** Water being dumped out of a helicopter tank and the distribution interval of water on the ground. (**a**) Helicopter hovering against the wind with the ground moving in the wind direction at wind speed. (**b**) Helicopter flying forward (forward flight speed = wind speed in a) with no wind and the ground fixed.

#### *4.4. Rule of Water Distribution on the Ground*

In accordance with the preceding data and calculation method, the region covered by water on the ground (also referred to as the water band in the literature) and average amount of water per unit area were given. Please note that, when calculating the average water amount per ground area, the accumulated water amount was considered in this paper instead of the water flow on the ground. However, in ANSYS FLUENT, the ground was set to have a non-slipping, fixed-wall condition, which, in this way, the water mass could flow all around after touching the ground; therefore, the accumulated water amount cannot be calculated automatically by this software. In order to calculate the accumulated water amount, the distribution of water mass just before touching the ground was taken into consideration in this paper, from which the water coverage area was given. Due to spatial–temporal changes in the water mass touching the ground, it is very complex to calculate the distribution of the water depth on the ground. Moreover, the breakup of drops and other phenomena were not taken into consideration in this paper; therefore, the average water depth was calculated in this paper only. Data on the hovering status of the helicopter, different wind speeds, the height of the tank bottom above the ground, the region covered by water on the ground, and the average amount of water were first provided, as shown in Table 1. The region covered by the water dump was approximated as a rectangle with area = longitudinal length × horizontal length. Table 1 shows that at wind speeds below 10 m/s, the region covered by water on the ground was basically not influenced by the wind, but when the wind speed reached 15 m/s, the longitudinal dimension of the region covered by water on the ground decreased slightly, whereas the horizontal dimension increased greatly. Therefore, the area covered increased greatly, and under the premise of an unchanged total amount of water, the average water depth accumulated per unit area decreased greatly. The higher the tank bottom was above the ground, the greater the area covered by water on the ground, and the less the average water depth accumulated per unit area. However, the results at a height of 10 m were significantly smaller than those at 20 m and 30 m, although the results at the latter two heights were relatively close to each other.

**Height of Tank bottom above the Ground/Wind Speed 0 m/s 5 m/s 10 m/s 15 m/s 10 m** 2.4 m <sup>×</sup> 1.6 m = 3.84 m2 0.29 m water depth/m2 2.2 m <sup>×</sup> 1.7 m = 3.74 m2 0.30 m water depth/m<sup>2</sup> 2.1 m <sup>×</sup> 1.7 m = 3.57 m2 0.31 m water depth/m2 2.1 m <sup>×</sup> 2.5 m = 5.25 m2 0.21 m water depth/m2 **20 m** 3.4 m <sup>×</sup> 3.0 m = 10.2 m2 0.11 m water depth/m2 3.2 m <sup>×</sup> 3.0 m = 9.6 m2 0.12 m water depth/m<sup>2</sup> 3.2 m × 3.2 m = 10.24 m2 0.11 m water depth/m2 4.0 m <sup>×</sup> 7.0 m = 28.0 m2 0.04 m water depth/m2 **30 m** 2.9 m <sup>×</sup> 2.9 m = 8.41 m2 0.13 m water depth/m2 3.0 m <sup>×</sup> 3.0 m = 9.0 m2 0.12 m water depth/m<sup>2</sup> 3.0 m <sup>×</sup> 3.0 m = 9.0 m2 0.12 m water depth/m2 5.0 m <sup>×</sup> 9.0 m = 45.0 m2 0.025 m water depth/m2

**Table 1.** Influence of wind speed and height of the tank bottom above the ground on the region covered by water and the average water amount on the ground while the helicopter was hovering.

As the helicopter flew forward, the region covered by water on the ground and the amount of water were also subject to the influence of forward flight speed. By the method discussed in Section 4.3, the average water distribution on the ground from the water dump when the helicopter flew forward (no wind) was as shown in Table 2. For forward flight, the higher the forward flight speed, the less the average water depth; a similar relation held for flight height. The average water depth per unit area was one order of magnitude less than in the cases of the corresponding hovering helicopter and wind speeds. For example, with a helicopter at a forward flight speed of 15 m/s and the tank bottom 30 m above the ground, the dumped water was distributed within a region of approximately 337.5 m2, and the average water depth accumulated in this region per square meter was 0.3 cm. There were two working conditions having similar premises. The working condition of Hayden Biggs [15] was the most similar, with a forward flight speed of 70 km/h, a tank water-carrying capacity of 1.4 t, and a height above the ground of 24 m. The range of the water band on the ground was 120 m × 21 m, and the average water depth was 0.34 cm. The average water depth under similar working conditions in the present study was 0.3 cm, showing good agreement. Another similar working condition was that of Xie Yingmin [12]. In this case, the flight speed was 60 km/h (equivalent to 16.67 m/s), the height was 30 m, and the wind speed was 3 m/s. Their results showed that the maximum water belt on the ground was 110 × 25 m, the effective water belt was 65 × 15 m, and average water depth was 0.1–0.3 cm. The water-carrying capacity of the tank in the study by Xie Yingmin et al. [12] was 3 t, which was almost three times that in the present study, and assuming that the outlet flow was the same, its corresponding water belt area was also about three times that in this study. Therefore, the results of this study were basically consistent with the working conditions in Xie Yingmin et al. [12].


**Table 2.** Average water distribution on the ground with the helicopter flying forward when making a water dump (no wind).

#### **5. Conclusions**

This study looked at two key parameters in firefighting helicopter operation: the height of the helicopter tank (H125/Isolair Eliminator II) above the ground (*H*) and the wind speed (*U*). After considering the relevant physical processes, such as the movement of water mass in the air, changes in the shape of the water mass, and the breakup of drops after water dump from the tank we decided to calculate the accumulated water amount on the ground. The height of the helicopter from the ground and the wind speed (or forward speed of the helicopter) are also important parameters influencing these physical processes, and hence were also considered in this work. The VOF model and adaptive mesh in ANSYS FLUENT were applied in this paper, which yielded the average water amount distributed on the ground after water dump from the helicopter. A study of the parameters influencing the water dump distribution was performed, considering *H* = 10 m, 20 m, and 30 m and *U* = 0 m/s, 5 m/s (Level 3), 10 m/s (Level 5), and 15 m/s (Level 7). The main conclusions were as follows:


The following suggestions can be drawn from our results: if only the depth of water accumulated per unit area on the ground is considered when performing water dump firefighting, the helicopter should have the lowest possible forward flight speed and flight height and should perform firefighting under low wind speed conditions.

#### **6. Future Work**

The results calculated in this study show that the model developed here could be used to study the distribution of a water dump out of a helicopter tank, which has basically met the engineering requirements for firefighting with water dumps out of helicopters. To distinguish the water and air phase interfaces more meticulously and accurately, finer meshes and a smaller mesh adaptation cell scale would be required. In the meantime, in combination with "VOF-to-DPM" and the turbulent SAS model, small water droplets at mm level could be traced. For the fine meshes used in this study, the maximum mesh cell under the helicopter tank was 0.2 m in size, and the minimum mesh adaptation cell was 0.05 m, with total numbers of mesh cells up to 2 million. Using 84 CPU of the three calculation nodes of "Milky Way One", for example, it would take 17 h to calculate 1900 time steps (1.9 s). To distinguish water droplets at 0.01 m level (small water droplets at mm level required no distinction and were realized with the VOF-to-DPM model), the number of mesh cells would have to be increased by 125 times approximately, to 200–300 million mesh cells. If 840 CPU of "Milky Way One" were used, it would take about 10 days to calculate 1900 time steps, or about 200,000 CPU hours. Therefore, such calculation could be realized, but at an enormous cost.

This paper is merely a preliminary study on belly firefighting tank water dumping by helicopter and ground water distribution, and a coupling fire-field model must also be investigated. In the complete process of helicopter water dump firefighting, the wake flow of the rotor wings, the water–air flow and droplet dynamics, and combustion and the heat and smoke generated are all involved, making this still a very challenging problem of how to use the above models to establish an effective numerical calculation scheme.

**Author Contributions:** Conceptualization, J.L.; methodology, T.Z., S.L.; validation, T.Z. and C.W.; formal analysis, T.Z.; investigation, S.L.; data curation, T.Z.; writing—original draft preparation, T.Z.; writing—review and editing, T.Z. and S.L.; visualization, T.Z.; supervision, T.Z.; funding acquisition, J.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by State Grid Corporation of China Science and Technology Project (5216A0210041) and the National Key Research and Development Plan (No. 2016YFC0800104).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** All data generated or analyzed are available on request through the author, Zhou Tejun, whose email address is zhoutejun1988@126.com.

**Acknowledgments:** The authors would like to thank the Editor and the reviewers for their comments and suggestions, which have been very helpful in improving the quality of this paper.

**Conflicts of Interest:** The authors declared that they have no conflicts of interest in this work.

#### **References**


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