Transportation and Reserve of Emergency Medical Supplies during Public Health Events

Abstract

When a public health event occurs, it is very difficult to guarantee a stable supply of emergency medical supplies; this has a great impact on the efficiency of emergency rescue work. Therefore, this paper takes the problem of transporting and stockpiling emergency medical supplies in modern public health events as its research theme. We use the SEIRD (susceptible, exposed, infected, recovered, and dead) system dynamics model to predict the number of infected people and the demand for emergency medical supplies and obtain a number of single-day demand of 0.3 N + 0.15 I − 0.15 R − 0.3 D. An index system based on 11 indicators was established and the demand urgency function was designed. A bi-objective vehicle routing problem with time windows (VRPWT) for emergency medical supplies considering demand urgency and response cost minimization is established and solved using particle swarm optimization (PSO). To test our approach, the model is simulated using the initial COVID-19 data of six cities in China. Finally, we obtain the prediction of these six demand points and the demand urgency, and the PSO algorithm can reach the optimal solution in this VRPTW problem. The optimal travelling distance is about 1461.45 km and the total cost is 6726.5 Yuan. This simulation confirms the model’s rational and feasibility and presents suggestions to cope with modern public health events.

1. Introduction

Public health issues refer to food events that pose serious harm to public health, major infectious diseases that can cause serious harm to public health or have caused serious harm to public health, and group diseases of unknown causes. Major events occur frequently in the field of public health. Examples include the following: the outbreak of severe acute respiratory syndrome (SARS) in 2003; the outbreak of the influenza A (H1N1) virus in April 2009, which took a huge toll on people across the globe; the emergence of the new crown epidemic and the start of outbreaks globally from December 2019, which has severely impacted people’s lives, health, and livelihoods; and the recent outbreak of the influenza A virus in 2023, which is likely to return in the foreseeable future. These public health incidents have not only seriously affected people’s health but have also had a negative economic impact on all walks of life. The supply-side reform was seriously slowed down and the total demand and supply dropped sharply in the short term. The capital chain of a large number of small and medium-sized enterprises is broken and bankrupt, which affects the economic circulation and employment. This had an impact on input–output efficiency, consumption pull rate, opening to the outside world and trade, tourism, catering, transportation, and other industries, which are directly and fatally affected.

The level of emergency management of public health emergencies is related to the happiness and safety of people. Emergency material support is the basic work of emergency management, and the timeliness and effectiveness of support have a direct impact on the effect of emergency support of public health emergencies. Since the outbreak of the “SARS” crisis, countries have attached great importance to the emergency response ability of public health emergencies and have accordingly improved the level of emergency support.

The COVID-19 epidemic is one of the most serious and difficult current public health issues. In the event of a regional outbreak, the general management of emergency medical supplies faces challenges such as low distribution efficiency and an imperfect warehouse emergency plan, which make it easy for the whole system to fall into a passive state. At the same time, in such public health incidents, there is a shortage of medical supplies in many places, such as “long queues in pharmacies to buy ibuprofen”, “soaring prices of N95 masks”, and “insufficient medicines in hospital warehouses” in the recent two years. The change in epidemic form has caused the shortage of emergency medical materials. In order to predict, prevent, and temporarily deal with this problem and eliminate the waste of materials, the transportation and reserve of emergency medical materials can effectively prevent the spread of the epidemic, focus on solving the short-board problem of material security in dealing with serious public health emergencies, and earnestly safeguard people’s lives, health, and safety. Whether emergency medical materials can be supplied in time directly affects the treatment rate and mortality rate of patients and is also a key factor to ensure the safety of people’s lives. However, most traditional material scheduling modes use demand points to increase demand and distribution centers to redistribute materials. This mode can only be relieved when problems occur and since there are many influencing factors scheduling often cannot meet expectations.

The pneumonia epidemic in COVID-19 has caused a general shortage of emergency materials all over the world, which has brought certain challenges to the scheduling, storage, and distribution of materials for public health emergencies. The advance mobilization and stockpiling of emergency medical supplies in the event of a public health incident is facing problems and challenges. Transportation and storage of emergency medical materials are of great significance and value in promoting the construction and improvement of the national emergency management system, improving the level of public health and safety, and protecting people’s health and safety. Designing a faster, more efficient, and less labor- and material-intensive mobilization reserve program is the research problem of this study. Therefore, our goal is to respond to emergency medical supplies before the large-scale outbreak of public health issues, scientifically and efficiently predict the outbreak of public health issues, and deal with the optimal route transportation and storage of emergency medical supplies in public health issues, to minimize the harm caused by public health issues.

The work process in this study goes as follows: First, a SEIRD model for modern public health issues was established and the least-squares method was used to fit the model parameters, thus completing the prediction of infection trends. Then, we defined the set of emergency medical supplies and combined the characteristics of different populations to predict the amount of emergency medical supplies needed on a single day. We then defined the urgency functions for outbreak prevention and control capacity and emergency medical supplies, outlined how the parameters are calculated, and determined the overall urgency function based on their respective weights. Then, a bi-objective vehicle path optimization problem with a time window considering demand urgency and minimum response cost was constructed and a particle swarm algorithm was used to solve the problem. Finally, a simulation test of the model is carried out to verify the feasibility and rationality of the model.

This paper is organized as follows: Section 2 presents the literature review, Section 3 establishes a model and designs a solution algorithm that can solve the problem of emergency medical material mobilization and stockpiling, Section 4 explores the effectiveness of the built model, Section 5 simulates the constructed model to confirm the feasibility of the model, Section 6 provides a discussion of the article, Section 7 proposes six countermeasures and recommendations, respectively, for the constructed model to effectively deal with public health issues, and Section 8 concludes the main findings.

2. Related Work

2.1. Development of Emergency Medical Supplies

Public health issues have the characteristics of rapid spread, urgency, and difficulty in prevention and control, which bring great challenges to the emergency management system. The shortage and surge of emergency medical supplies in various locations are the main reasons that restrict the emergency management system and solutions to public health issues [1]. Emergency medical materials play a decisive role in the prevention and control of public health issues and their irreplaceability, timeliness, and lag make them an important guarantee for treating patients and slowing down the spread of epidemic situation. Therefore, to prepare for an unpredictable sudden epidemic situation, rational allocation of medical materials and emergency dispatch have become a basic work in epidemic prevention and control [2]. Zhou and other scholars have studied the inventory control system of a national medical reserve for rotation of emergency medical materials [3] to deal with long-term serious expiration of emergency medical materials, maximize the use of hospital emergency resources, and comprehensively improve the ability to deal with public health emergencies. Considering the reserve of emergency medical materials, Zhang, Shi, and other scholars have studied a capital reserve mode, which is different from the physical warehouse reserve [4], and have come to the conclusion that the increase in demand uncertainty sometimes leads to a decrease in the level of safety stock, although the comprehensive reserve does increase. In this case, in order to limit the risk of obsolescence of emergency medical supplies and reduce dependence on safety stock, it is best to increase dependence on capital reserve. The emergency dispatch management of medical materials can be thoroughly studied and optimized [5] to reduce the adverse effects caused by inadequate supply of medical materials and improve the efficiency of emergency rescue of medical materials. Moreover, in the process of prevention and control of pneumonia in COVID-19, there is a shortage of medical materials in all countries, which reflects that the current emergency medical materials dispatching system in all countries is still insufficient [6].

2.2. Demand Forecasting Model for Emergency Supplies and its Solution Algorithm

First, Stăncioi, C.-M., and other scholars have developed a mathematical model for the COVID-19 pandemic dynamics to predict the trends; the outputs of the model are the number of new cases, the number of new deaths, the total number of cases, or the total number of deaths [7]. Shin, H.H., and others constructed a SEIR-H epidemiological model for the spread dynamics in a given population [8]. This model extends the SEIR model, while researchers have carried out parameter simulation and estimation work, using Paraguay as a case study. Nistal, R., and others designed two SEIR models for the COVID-19 incidence study in Europe. Among them, the extended SEIR model can describe all kinds of populations more accurately, but it is cumbersome to operate, while the μ-SEIR model is simpler, but the results are not very accurate [9]. Hachiya, D., and other scholars studied the path planning for emergency supplies transportation based on drone technology, which takes into account the multi-objective, multi-trip, multi-item, and multi-UAV problems, and the model improves the stability of the emergency supplies supply [10]. In the case of fuzzy or missing data the demand forecasting of emergency supplies will become difficult; Zhang, M., and other scholars proposed two computational formulas solving “core” of fuzzy interval grey numbers and established a demand prediction model for emergency supplies, which has high prediction accuracy [11]. Ren, X., and other scholars proposed a dynamic vehicle path problem for the characteristics of sudden-onset epidemics with the distribution of regional emergency supplies as the research object, and finally solved the problem using the SFSSA algorithm, which provided a solution to the problem [12]. Some scholars have studied the multicycle site selection-distribution model of integrated disposal of emergency medical materials and infected patients in epidemic situations, and have proposed the multicycle site selection-allocation model to allocate emergency hospitals, allocate emergency medical materials, and dynamically integrate disposal of infected patients [13]. Yang, M., and other scholars developed a new multi-period dynamic pre-positioning method for emergency supplies for disaster mitigation, and verified the validity of the model based on simulation [14]. Kamar, A., and other scholars conducted a comparative assessment of three surge calculators for COVID-19 using Lebanon as an example to emphasize that the prediction of COVID-19 remains challenging [15]. Zhang, H., and other scholars consider the constraints of UAV performance constraints, airspace constraints, and allocation constraints, and utilize an improved simulated annealing algorithm to model a demand-based UAV scheduling scheme, which is helpful for the scheduling problem of emergency supplies [16].

VRP can be used to solve the transportation and storage of emergency medical materials. In 1959, D and R first proposed the vehicle routing problem (VRP) [17], which means that under a certain number of demand points, each vehicle should plan its own driving route to meet the requirements and achieve the goals of shortest distance, minimum cost, and minimum time consumption. It involves various relationships between transportation enterprises and customers. Among them, Thangiah [18] and Joe [19] solved the VRPTW problem by using a genetic algorithm. Fisher uses MINIMUMK-TREES to solve the vehicle routing problem, which can be modeled as the problem of finding a minimum-cost K-tree [20]. Song, W., and other scholars proposed an improved ant colony algorithm (ACA) solution model for the VRPTW problem in community group purchasing to provide help in solving this kind of problem [21]. Saksuriya, P., and other scholars have designed a new specific heuristic algorithm for solving the VRPTW problem with compatibility constraints in home healthcare systems. This heuristic algorithm is an efficient hybrid of a novice local search (LS), ruin and recreate procedure (R&R) and particle swarm optimization (PSO). This heuristic algorithm can solve this VRPTW problem efficiently [22]. Díaz de León-Hicks, E., and other scholars investigated the use of method selection that can solve the VRPTW problem. The researchers compared an attention-based meta-learner method with five models: multi-layer perceptron, k-nearest neighbors, softmax regression, support vector machines, and decision trees. This work contributes to the development of neural network algorithms [23].

Dealing with public health issues usually involves prevention, control, treatment, and rehabilitation. Unlike previous public health emergencies, this epidemic shows the characteristics of modern public health issues. First, citizens pay more attention to personal hygiene and to their own health. Second, the virus mutation rate is high, which makes it easy to produce other types of viruses and difficult to control. It is more difficult to control than in the past, and it is urgent to predict and prevent them. Third, there are differences in measurements between China and other countries. China has made great efforts to prevent it and implemented the policy of “releasing input from outside and preventing rebound from inside”.

In summary, scholars at home and abroad have been involved in the research of emergency medical materials transportation and storage in modern public health issues, but the transportation and storage algorithms still follow the previous methods, and many novel and efficient metaheuristic algorithms have emerged. Furthermore, public health issues in the new era have their own characteristics, and new policies have emerged in the world to deal with new public health issues, so it is of practical significance to study the transportation and storage of emergency medical materials.

3. Materials and Methods

3.1. Forecast of Emergency Medical Supply Demand and Model for Mobilization and Stockpiling

3.1.1. Prediction Model of Infected People Based on SEIRD

The SEIR (susceptible, exposed, infectious, recovered) model, as the most basic system dynamics model of infectious diseases [24], studies the dynamic mechanism of infectious diseases in the transmission process and provides a theoretical basis for the prevention and treatment of infectious diseases. The SEIR epidemic model can effectively simulate public health issues. Basic public health event models of infectious diseases include SI, SIR, SIRS, SEIR, etc. In order to solve the models, ordinary differential equations, partial differential equations, and network dynamics are studied. Based on the SEIR model and considering the new characteristics of modern public health issues, this paper assumes that the new identity D stands for Dead. There are also many unfortunate deaths in modern public health issues, and the inclusion of the new identity D in the model allows the model to simulate a situation that is more closely related to a modern public health issue, without increasing the computational complexity of the model. The SIERD model is more plausible than the SEIR model. In addition, there are many other methods for prediction of public health event situations, such as deep ensemble learning methods for COVID-19 prediction [25]. This method requires training of the model and produces a model with high accuracy in predicting results but is not model specific and requires a large data base. There are also studies that estimate COVID-19 trends using the ARIMA model, which consists of an autoregressive (AR), integral (I), and moving average (MA) model [26,27]. However, the model requires a static time series and lacks accuracy in the early stages of time and lacks advantages in its wide application to the prediction of public health issues. Normally the SEIRD model is simpler to fit, and the formula is more intuitive. However, the SEIRD model has certain requirements on the setting of parameters, which need to be supported by scientific data to fit, such as the parameter “latency period”, which should also be set in conjunction with the actual clinical research. This paper is a comprehensive study of public health issues. The SEIRD model has a wider applicability, and the data format of the prediction is five categories of people, which brings convenience to the subsequent prediction of the demand for emergency medical supplies in this paper. Therefore, the SEIRD model is more applicable to the context of this paper. Although modern public health issues have the characteristics of a long latent period, the SEIRD model can simulate modern public health issues more appropriately, among which the following are:

S stands for Susceptible, which refers to a person who is not yet sick but is susceptible to the virus and will become an “E” sometime after being infected by an “I”;

E stands for Exposed, which refers to the person who has been in contact with an infected person but is temporarily unable to infect others. Such people carry a virus and have a certain incubation period and will become a susceptible person;

I stands for Infectious, which refers to a person infected with the virus who is already sick and who can transmit the virus to susceptible people and convert them into members of class E;

R stands for Recovered, which refers to a person who has been quarantined from the system, or who has recovered, and who will not be infected;

D stands for Dead, which refers to a person who has died during the event and cannot be turned into another type of identity.

And make the following assumptions:

• The susceptible person does not have the possibility of infection when contacting the Exposed, that is, the Exposed will not infect the susceptible person;
• The susceptible person has the possibility of infection after contact with the susceptible person;
• Recovered patients have lifelong immunity. As long as they are cured, they will not be infected again;
• The death population is not infectious;
• The total population remains unchanged during public health issues;
• Only communication between people is considered and environmental communication is not considered;
• At the beginning of public health issues, the number of recovered persons and the number of dead persons were 0.

Among them, the susceptible person (S) will be infected by the infectious person (I) to become the exposed person (E). The exposed person (E) will become the infectious person (I) after a period of time, and the infectious person (I) will become the recovered person (R) or the dead person (D) after treatment.

The specific relationship is shown in Figure 1.

According to the relationship between the SEIRD model and its variables, the following differential equations are constructed:

$$\left\{\begin{array}{c}\frac{dS}{dt}=-\frac{\beta \times I(t)\times S(t)}{N}\\ \frac{dE}{dt}=-\zeta \times E(t)+\frac{\beta \times I(t)\times S(t)}{N}\\ \frac{dI}{dt}=\zeta \times E(t)-\gamma \times I\left(t-{\tau }_r\right)-\mu \times I\left(t-{\tau }_d\right)\\ \frac{dR}{dt}=\gamma \times I\left(t-{\tau }_r\right)\\ \frac{dD}{dt}=\mu \times I\left(t-{\tau }_d\right)\end{array}\right.$$

(1)

Among them:

• S refers to susceptible people, E refers to exposed people, I refers to infected people, R refers to recovered people, D refers to dead people, and N refers to the total number;
• t represents the current time;
• β indicates the probability that susceptible people will be converted into exposed people after contacting infected people per unit of time;
• 1/ζ indicates the average latent period, and people with ζ × E(t) per unit time change from exposed people to infected people;
• γ Indicates the cure rate and the γ × I(t − τ_r) people change from infected to recovered people in unit time t;
• μ Indicates the mortality rate and the μ × I(t − τ_d) people change from infected to dead people in unit time t.

Time delay τ_r and τ_d are used for rehabilitation (cure) and death, respectively. Usually, because the epidemic time is very short, it is assumed that the net impact of birth and natural death is zero. Without considering various factors such as birth, natural death, immigration, and emigration, it is assumed that the total number of people N remains unchanged, and the number of people of various types at T time is recorded as S(T), E(T), I(T), R(T), and D(T), respectively, then N = S(T) + E(T) + I(T) + R(T) + D(T). To solve the differential equations, transform them into iterative models:

$$dS=-\frac{\beta \times I\left(t\right)\times S\left(t\right)}{N}dt$$

(2)

Move items to obtain:

Integrate t from n − 1 to n at both ends of the equation:

$${\displaystyle {\int }_{n-1}^{n}dS}={\displaystyle {\int }_{n-1}^n-}\frac{\beta \times I\left(t\right)\times S\left(t\right)}{N}dt$$

(3)

From the left matrix formula: ${\int }_a^{b}g\left(x\right)\approx (b-a)g\left(a\right)$

$$S_n=S_{n-1}-\frac{\beta \times I_{n-1}\times S_{n-1}}{N}$$

(4)

In the same way, the residual equation can be obtained:

$$E_n=E_{n-1}+\frac{\beta \times I_{n-1}\times E_{n-1}}{N}-\zeta \times E_{n-1}$$

(5)

$$I_n=I_{n-1}+\zeta \times E_{n-1}-\gamma \times I_{n-1}-\mu \times I_{n-1}$$

(6)

$$R_n=R_{n-1}+\gamma \times I_{n-1}$$

(7)

$$D_n=D_{n-1}+\mu \times I_{n-1}$$

(8)

3.1.2. Coefficient Fitting

In this paper, the unit time is set as day (d). To solve the differential equations, it is necessary to estimate the parameters of the equations. In the SEIRD model, the average latency period 1/ζ parameter needs to be obtained after a large number of disease data statistics and set to the corresponding value, and the total population number N parameter also needs to be set directly according to the actual. In order to obtain a more accurate and applicable model, the coefficients β, γ, and μ of the differential equations need to be fitted using the least-squares method, and the establishment of the SEIRD model is thus completed.

3.2. Model of Forecast Demand for Emergency Medical Materials

Emergency medical materials generally refer to the urgently needed medical materials for the treatment of infected patients and injured people after disasters when various emergencies occur [28]. Emergency medical materials are one of the urgently needed materials that need emergency input after emergencies. Taking as an example the need for emergency medical materials in COVID-19, the types of emergency medical materials are, but are not limited to, the following categories [29]:

• Medical supplies, such as medical masks, protective clothing, goggles, gloves, disinfectant, thermometers, medicines, and first aid kits;
• Rescue equipment: mainly construction machinery, excavators, bulldozers, loaders, dump trucks, tankers, generator sets, and medical waste treatment equipment;
• Communication equipment: including radio communication equipment, wired communication equipment, etc.;
• Living security materials, mainly tents, folding beds, sleeping bags, inflatable mattresses, folding tables and chairs, portable stoves, emergency lights, folding buckets, plastic buckets, garbage bags, and food.

To predict the demand for emergency medical materials, it is necessary to predict the number of people according to Section 3.1, combined with the urgent needs of various groups of people for consumable medical materials in the early stages of the epidemic. Due to the lack of uniform and effective personnel classification methods and standards, there are many problems in large-scale population evacuation. Considering the complexity of the amount of emergency materials needed by different people in a single day in the SEIRD model, we set the model by directly defining the emergency medical materials group θ [30]. In view of the ambiguity of the actual observation of the susceptible population (S) and the exposed population (E), we classified these two groups as the susceptible population (S) and drew the conclusion that S = (N − I − R − D). Therefore, the hypothesis is established as shown in

Table 1. Assumption on the Demands for Emergency Medical Materials.

Crowd Category	Number of People	Demand	Total Demand
Susceptible (S)	N − I − R − D	2θ	2θ(N − I − R − D)
Infectious (I)	I	3θ	3θI
Recovered (R)	R	θ	θR
Dead (D)	D	0	0

.

According to the epidemic experience, the daily demand for each infected person is 3θI. The daily demand of each susceptible person is 2θ(N − I − R − D). The demand of each recovered person in a single day is θR. At the same time, the daily consumption index and the proportion of daily demand for different types of infection were formulated. Through calculation, the daily consumption of various items is obtained: In a single day the demand for medical surgical masks weighing approximately 18 grams by the cured population is 2. The number of disposable gloves with a weight of approximately 4 grams is three sets. The 75 grams of goggles are required every day. The demand for disinfection products weighing approximately 27 grams is 30 mL (containing alcohol and antibacterial hand gel). Disposable gloves and goggles are mainly used to isolate patients and infected persons during the epidemic, while alcohol and disinfectant are used to treat or care for patients, which are the most commonly used drugs in hospitals. The total weight is 150 g, and the daily emergency medical supplies required by a single person in kilograms are 0.15, that is, the set θ = 0.15, so the daily total demand for susceptible people is 0.3(N − I − R − D), the daily total demand for infected people is 0.45 I and the daily total demand for cured people is 0.15 R.

3.3. Allocation and Storage Model of Emergency Medical Materials

In order to simulate the demand for medical materials in an emergency and provide a quantifiable description of the research content, this paper designs a demand urgency function. To reflect the demand for each demand point for emergency medical materials, it is necessary to use a weight index to determine the priority order of distribution among different demand points. To minimize the delay loss and total cost of each demand point, a stochastic programming model for emergency materials scheduling is established and the optimal solution is obtained by solving this problem. When a public health incident occurs, facing an emergency, the transportation and storage of emergency medical materials should face the latest service window to implement rescue as soon as possible. As the geographical location and environmental conditions of each demand point are quite different and are obviously affected by the external environment, the problem is complex. On the premise of considering the actual situation of the epidemic situation, if the delivery time window is later than the demand point and the material supply is insufficient, it will lead to a delay in personnel treatment, which will generate more costs and affect the lives and health of people in the disaster areas. With the delay time, the cost of delay punishment would be higher. To complete material assistance within the best satisfactory time window for each demand point and reduce the overall cost of delay penalty [31], it is necessary to design a penalty function to determine the priority of distribution.

3.3.1. Demand Urgency Function

The urgency of the demand is the degree to which a certain demand point needs help for public health issues according to its own situation. To design the demand urgency function, it is necessary to first determine the influencing factors and weights. Because there are many factors of public health issues that affect the urgency of demand, to select the main influencing factors and perform quantitative analysis, principal component analysis was used to study the main factors affecting the ability to prevent and control epidemics.

According to the requirements of the National Emergency Plan for Public Health Emergencies, the Law of the People’s Republic of China on the Prevention and Control of Infectious Diseases, the Emergency Response Law of the People’s Republic of China, the Novel Coronavirus Diagnosis and Treatment Plan, and related documents [32,33], combined with the actual situation of countries around the world dealing with SARS-CoV-2, the corresponding evaluation index system is presented [34] in order to facilitate the citation of data and refer to the data format of the statistical yearbook, as shown in

Table 2. Evaluation Index System.

Target Layer	Guideline Layer	Indicator Layer
Public health event prevention and control capabilities	Dissemination channels	X1 population density (people/km2)
		X2 strictness of prevention and control policy
		X3 receives inbound tourists
	Population susceptibility	X4 enrollment rate of institutions of higher learning (%)
		X5 median age
		X6 vaccination rate (%)
	Responsiveness	X7 number of beds for thousands of people (sheets/thousands of people)
		X8 GDP per capita (US $10,000)
		X9 health expenditure as a percentage of GDP (%)
		X10 consumer Spending as a percentage of GDP (%)
		X11 UHC coverage index

.

Among them, the strict index of X2 prevention and control policy is calculated from eight indicators: “whether to close primary and secondary schools and universities”, “whether to close workplaces”, “whether to cancel public activities”, “whether to stop public transportation”, “order to take refuge on the spot or isolate at home”, “restriction on internal mobility between cities/regions”, and “restriction on international travel”. The X11 UHC coverage index refers to the universal health coverage index.

In order to establish a scientific and standardized demand urgency function, the evaluation index system needs to be subjected to principal component analysis to extract more effective principal components. Assuming that m principal components are extracted, let the percentage of principal component contribution be a_i and the percentage of principal components accounted for by the 11 indicators in the evaluation index system be b_ij. X_ik(t) represents the value of the Xi indicator at demand point k at moment t.

Therefore, based on the weight of classification indicators, this paper designs the urgency function of demand of the prevention and control ability of epidemics. If the urgency of the demand for epidemic prevention and control ability in a certain area is Y_1k(t), the formula of the urgency of the demand for epidemic prevention and control ability in a certain area is obtained:

$$y_{1k}(t)={\displaystyle \sum _{i=1}^{\mathrm{m}}{a}_i}{\displaystyle \sum _{j=1}^{11}{x}_{ik}(t)\times b_{ij}}$$

(9)

Finally, normalized treatment is performed and Y_1K represents the urgency of epidemic prevention and control ability in the k-th region among n regions.

$$Y_{1k}=\frac{y_{1k}}{{\displaystyle \sum _{i=1}^n{y}_{1i}}}$$

(10)

According to the development of an epidemic situation and the need for emergency medical materials, the urgency function of the emergency medical materials demand is designed. In Equation (11), N denotes the number of the total population at demand point k at time t; I denotes the number of the infected population at demand point k at time t; R denotes the number of the recovered population at demand point k at time t; and D denotes the number of the dead population at demand point k at time t. If the urgency degree of emergency medical material demand in a certain area is Y_2k(t), the formula of emergency medical material demand urgency degree in a certain area is obtained:

$$y_{2k}(t)=0.3N+0.15I-0.15R-0.3D$$

(11)

Finally, normalized processing is performed, and Y_2K represents the urgency of the demand for emergency medical materials in the k-th region among n regions.

$$Y_{2k}=\frac{y_{2k}}{{\displaystyle \sum _{i=1}^n{y}_{2i}}}$$

(12)

The higher the urgency of the demand for epidemic prevention and control ability, the better the situation of epidemic prevention and control in this area. That is, the higher Y₁ proves that the demand for epidemic prevention and control is low and the higher the urgency of the demand for emergency medical materials, the worse the demand for emergency medical materials in this area. That is, the higher Y₂ proves the high demand for emergency medical materials. Mathematical processing is performed to design the total demand urgency function Y as follows:

$$Y_k=-{\phi }_1\times Y_{1k}+{\phi }_2\times Y_{2k}$$

(13)

where φ₁ is the weight of the urgency function of the demand of the ability to prevent and control epidemics, and φ₂ is the weight of the urgency function of the demand of emergency medical materials.

3.3.2. Allocation and Storage Model of Emergency Medical Materials

The purpose of this paper is to study how to optimize the transportation and storage of emergency medical materials at a lower cost based on the requirements of time and demand. Emergency medical materials have the characteristics of various types, large quantities, and high transportation timeliness. However, in public health emergencies, such as epidemics, the demand for emergency medical materials is always uncertain and urgent. Every rescue has a golden age, and timely delivery of emergency medical supplies will greatly protect the lives and health of victims. At the same time, with the gradual development of Internet technology, timely information is the basic requirement, which requires the establishment of a perfect emergency medical materials distribution system to deal with the impact of emergencies. Therefore, in the scheduling and storage model, the most important thing is the urgency of the demand for each demand point, aiming to minimize the comprehensive delay penalty cost of each demand point and to meet the best service time window of each demand point as much as possible. At the same time, according to the characteristic that the demand for emergency medical materials varies greatly in different regions, an emergency medical materials dispatching model based on fuzzy multi-attribute decision-making method is constructed, which can well adapt to the emergency medical materials dispatch requirements in different regions. Taking an emergency medical material distribution center as an example, this paper studies its dispatching problem. When the demand emergency degree is low, the emergency degree level is higher, so it should give priority to meeting its best service time window.

Therefore, in order to achieve the goal of minimizing the cost and the shortest response time, a dual-objective function is proposed to reduce the overall running time of the system and reduce the penalty cost of each demand point to achieve the goal of minimizing the cost and the shortest response time. A dual-objective optimization model is established to optimize the distribution route.

H = (0, 1, 2, 3,…, h) is the demand point, where H₀ is the center of the dispatching point of emergency medical supplies. The existing emergency medical materials in the center of the dispatching point is V₀. The number of vehicles that can be dispatched is K. The maximum load of a vehicle is q₀, and there is no fault problem in the vehicle. D = {d(a,b)│a,b∈H} is the distance set between various demand points, d(a,b) represents the distance from a to b, $t_{ab}^k$ represents the time it takes for vehicle K to be dispatched from a to b, and v₀ represents the driving speed of the distribution vehicles. C₀ represents the cost per unit distance of vehicle K, C₁ represents the start-up cost of vehicle K, ET_a represents the earliest service time acceptable to demand point a, RT_a represents the last service time acceptable to demand point a, ∆_a represents the assembly time required by demand point a, q_a represents the quantity of emergency medical materials required by demand point a, Y_a represents the total urgency of demand corresponding to demand point a, B_a represents the delay time caused by emergency medical materials reaching demand point a, D_a represents the penalty cost caused by emergency medical materials reaching demand point a, and o represents the penalty cost per unit time when the latest acceptable service time is exceeded.

Set decision variables:

$$x_{ak}=\left\{\begin{array}{l}1,\mathrm{Materials} \mathrm{for} \mathrm{demand} \mathrm{point} a \mathrm{are} \mathrm{delivered} \mathrm{by} \mathrm{vehicle} k\\ 0,\mathrm{Materials} \mathrm{for} \mathrm{demand} \mathrm{point} a \mathrm{are} \mathrm{not} \mathrm{distributed} \mathrm{by} \mathrm{vehicle} k\end{array}\right.$$

$$u_{abk}=\left\{\begin{array}{l}1,\mathrm{Vehicle} k \mathrm{transports} \mathrm{material} \mathrm{from} a \mathrm{to} b\\ 0,\mathrm{Vehicle} k \mathrm{does} \mathrm{not} \mathrm{transport} \mathrm{material} \mathrm{from} a \mathrm{to} b\end{array}\right.$$

Under normal circumstances, the distribution center must deliver emergency medical materials within the time window ET_a to RT_a of the material demand point. In this paper, the emergency medical logistics path optimization model is constructed with the objective function of minimizing total transportation cost, and the particle swarm optimization (PSO) algorithm is designed to solve the model. In view of the high consumption of emergency medical materials needed during public health issues, the large scale of use, and the strong emergency demand, the waiting cost caused by the early arrival of vehicles is not taken into account. By establishing a mathematical model, this paper studies the best route selection of emergency medical materials in different situations. If the delivery vehicle arrives at the demand point beyond the latest time window during rescue, resulting in insufficient supply of emergency medical materials, thus affecting life and health and prevention and control of public health issues, the emergency logistics system should be punished. If the urgency of the demand for service is greater, the total delay time will be longer, and the corresponding punishment cost will also increase. In this paper, the reduction in delay loss is taken as the optimization objective to establish a model, and a particle swarm optimization algorithm is designed to solve it. The following is the B_a formula to describe the sum of delay times:

$$B_{\mathrm{a}}=\left\{\begin{array}{ll}{\displaystyle \sum _{k=1}^K{T}_{ak}{x}_{ak}}-R{T}_a& {\displaystyle \sum _{k=1}^K{T}_{ak}{x}_{ak}}\ge R{T}_a\\ 0& {\displaystyle \sum _{k=1}^K{T}_{ak}{x}_{ak}}<R{T}_a\end{array}\right.$$

(14)

The resulting penalty cost D_a formula is as follows:

$$D_a=o\times Y_a\times \max [B_a,0]$$

(15)

The total running time of the system refers to the total time required for all vehicles to complete the distribution of emergency medical materials according to the path generated by the calculation and solution at the beginning of the system, including the service time for the assembly and transport of the materials, and then returning to the distribution center collectively. If we set the total system time to T, then we can use the T formula to express it:

$$T={\displaystyle \sum _{k=1}^K{\displaystyle \sum _{a=1}^h{\displaystyle \sum _{b=1}^h{t}_{ab}^k{u}_{abk}}+{\displaystyle \sum _{a=1}^h{\Delta }_a}}}$$

(16)

Then the cost function Z₂ for vehicle travel is as follows:

$$Z_2=c_1+c_0{v}_0{\displaystyle \sum _{k=1}^K{\displaystyle \sum _{a=1}^h{\displaystyle \sum _{b=1}^h{t}_{ab}^k{u}_{abk}}}}=c_1+{\displaystyle \sum _{k=1}^K{\displaystyle \sum _{a=1}^h{\displaystyle \sum _{b=1}^h{c}_0{d}_{ab}{u}_{abk}}}}$$

(17)

Based on the above assumptions, this paper proposes a bi-objective path optimization function, which aims to minimize the penalty cost of each demand point and the overall running time of the system. To conveniently solve the problem, the bi-objective problem is transformed into a single-objective problem, and the weights p₁ and p₂ (p₁ + p₂ = 1) are designed to obtain the optimal single-objective model as follows:

$$\min Z_1=\min {\displaystyle \sum _{a=1}^h{D}_a}=\min \left({\displaystyle \sum _{a=1}^{h}o{y}_a}\max [{\displaystyle \sum _{k=1}^K{T}_{ak}{x}_{ak}}-R{T}_a,0]\right)$$

(18)

$$\min Z_2=\min \left(c_1+{\displaystyle \sum _{a=1}^h{\displaystyle \sum _{b=1}^h{\displaystyle \sum _{k=1}^K{c}_0{d}_{ab}{u}_{abk}}}}\right)$$

(19)

$$\min Z=p_1\min Z_1+p_2\min Z_2$$

(20)

Among them, (18) is the penalty minimum objective function, (19) is the vehicle cost minimum function with the minimum total operating time of the system, and (20) is the single objective function with added weight.

Create constraints as follows:

$$s.t.\left\{\begin{array}{l}{\displaystyle \sum _{a=1}^h{\displaystyle \sum _{k=1}^K{u}_{0ak}}\le K}\\ {\displaystyle \sum _{a=0}^h{u}_{abk}}\le 1\\ {\displaystyle \sum _{k=1}^K{q}_{ak}}\le q_a\\ {\displaystyle \sum _{a=1}^h{q}_{ak}}\le q_k\\ B_{ak}\le x_{ak}\times \infty \\ {\displaystyle \sum _{b=1}^h{\displaystyle \sum _{k=1}^K{u}_{0bk}={\displaystyle \sum _{a=1}^h{\displaystyle \sum _{k=1}^K{u}_{a0k}}}}}\\ T_{bk}=(T_{ak}+{\Delta }_a+t_{ab}^k)u_{abk}\end{array}\right.$$

(21)

Constraint 1 indicates that the number of distribution vehicles in use is less than the total number of vehicles, Constraint 2 indicates that each transport vehicle can only pass through the demand point once, Constraint 3 indicates that the number of emergency medical materials on the vehicle in transport does not exceed the number of materials needed at the demand point, Constraint 4 indicates that the quantity of each delivery does not exceed the single deliverable quantity of the vehicle, Constraint 5 indicates that there is a certain range of delivery time, Constraint 6 indicates that the number of vehicles participating in distribution in the system is constant and plays a record role, and Constraint 7 represents the time when the vehicle k actually arrives at the demand point b.

3.3.3. Solving the Model

Since Savelsbergh proved that vehicle routing problems with time windows (VRPTW) is a NP-hard problem [35], research on this problem has focused mainly on various heuristic algorithms. In the vehicle distribution problem (VRP), heuristic algorithms have shown great advantages in problem solution selection and algorithm runtime [36]. Metaheuristic algorithms are similar to heuristic algorithms, but metaheuristic algorithms consider more important local optimality problems. Among them, PSO algorithm can be used to solve high uncertainty multi-objective optimization problems [37]. Moreover, PSO algorithm has proved to be a very effective method for solving vehicle path-related problems with more easily configurable parameters and wider applicability [38]. The metaheuristic algorithm is an improved scheme of the heuristic algorithm. Meta-heuristic algorithms mainly include Tabu algorithm, simulated annealing, genetic algorithm, ant colony optimization, particle swarm optimization, hybrid jumping frog algorithm, and artificial neural network algorithm [39].

In 1995, Kennedy and Eberhart [40] proposed PSO. Meta-heuristic algorithms are simple, parallel, and adaptive and can effectively solve some combinatorial optimization problems in practical applications. Therefore, more and more researchers attach importance to it.

In order to solve the above model, the PSO algorithm can be used for calculation. PSO is based on swarm to achieve the global optimum and then obtain the approximate optimal solution of the model. See

Table 3. Explanation of particle swarm optimization nouns.

Name	Meaning
Particle	Candidate solutions to optimization problems
Position	The location of the candidate solution
Speed	Speed of candidate solution movement
Fitness	The value for evaluating the advantages and disadvantages of particles is generally set as the objective function value
Individual optimal position	The best position found so far for a single particle
Optimal location for groups	The best position found so far for all particles

for an explanation of relevant terms, and use Python code for particle swarm optimization.

PSO is used to simulate the behavior of birds in the process of randomly searching for food. It is a globally convergent intelligent search algorithm. In PSO, the potential solution of each optimization problem is regarded as a bird in the search space, which is called “microparticle”. By updating the position, size, and flying height of particles, the population can reach the optimal solution or approximate optimal solution. The “flight” direction and distance of each particle are determined by the fitness value determined by an optimized function, while the speed of each particle determines their flight state.

PSO is initialized as a group of random particles that constantly seek the optimal solution in the iterative process to achieve the optimal effect. In this paper, a new adaptive particle swarm optimization method is presented, which uses a fast search strategy to optimize each particle locally in each iteration to improve convergence speed and accuracy. In each iteration, the particle will update itself by tracking two extremes, the first of which is the optimal solution discovered by the particle itself; that is, the individual extreme value. The second is the optimal value of the current particle at a new position found in the previous search area, which is called the group extreme value. The optimal solution found by the current population is called global extremum. In this case, if all the particles can be optimized, it is necessary to add some new parameters, called group extremum. Local extremum is a method that does not use the whole population but takes a part of it as the neighbor of particles to achieve the optimization effect.

Not depending on the problem itself, it has high efficiency and good robustness in solving complex optimization problems. The i-th particle is denoted x_i = (x_i1, x_i2,…, x_iD) and it has reached the optimal solution (with the best fitness) and is denoted as p_i= (p_i1, p_i2,…, p_iD), which is also called p_best. Thus, multiple populations with different fitness values are produced. The total optimum position of all particles in the population is set to p_g, also known as g_best. In this way, the optimum solution can be selected by calculating the fitness value of particle swarm optimization or by making it approach the global extremum to the maximum extent. The velocity of particle I is expressed as v_i = (v_i1, v_i2,…, v_iD). Each individual is an independent particle, and its motion state and environmental conditions change over time. For each generation, its d dimension (1 ≤ d ≤ D) will be adjusted according to the following equation:

$$v_{id}=w\times v_{id}+c_1\times rand()\times (p_{id}-x_{id})+c_2\times rand()\times (p_{id}-x_{id})$$

(22)

$$x_{id}=x_{id}+v_{id}$$

(23)

Each particle has a unique identification, which is called the first particle. In addition, the velocity V_i of the particles is limited by a maximum velocity V_max, which limits the speed at which they move. When a particle is subjected to an external force, its motion can be realized by changing its own acceleration. In Equation (22) w is the inertia weight, c₁ and c₂ are the acceleration constants, and rand() is a random value that varies in the range [0, 1]. For Formula (22), the previous paragraph of the formula discusses the inertia of the previous behavior of particles, and the second part of the formula belongs to the cognitive level of particles themselves. Among them, at the micro level, particles can share information or help each other to promote the overall progress, and the “cognitive” part includes the particles’ own understanding of the world around them and their responses to changes in the external environment. Thorndike’s law of effect can explain the “cognitive” part; that is, it is more likely that there will be enhanced random behavior in the future. Both parts establish theories about the possibility of creating new particles during the movement of particles and the change in the size and number of such particles. In this model, similar to the learning process, behavior is considered as a kind of “cognition”, and it is assumed that correct knowledge is obtained by strengthening the incentives of particles to reduce errors. The “social” part means that this model assumes that all behaviors can be influenced by some substitute variable to enhance their utility. Other particles will mimic the cognitive style of the particles themselves.

The flow of the standard PSO algorithm is as follows:

• Initialize a batch of particles (M-sized), including their random positions and velocities;
• Evaluate the adaptability of each particle;
• For each particle, we compare its fitness value with its best position p_best, and if its performance is better, it is considered the best position p_best at the current best position p_best;
• Each particle will compare its fitness value with the global optimal position g_best and, if the result is better, reset the index of g_best;
• According to the mathematical Formula (1), the speed of motion and the position of the particles will change;
• If the optimal condition for jumping out of the loop is not reached, return to step 2 [41].

The parameters of the PSO algorithm include the initial population size m, the set inertia weight w, the maximum velocity V_max of the acceleration constants c₁ and c₂, and the maximum algebra G_max.

The precision of V_max determines the resolution of the area between the current position and the best position. To improve the efficiency of searching the particles for the optimal set of solutions, a new method based on the dynamic threshold selection strategy and the improved least-squares support vector machine algorithm is proposed to solve this problem. When V_max is too high, particles may fall into the local optimal solution in the process of exploration, while when V_max is too small, particles cannot fully explore, thus falling into the local optimal solution. The main purpose of this restriction is to prevent data overflow in the calculation process, to perform manual intervention and change in learning attitude in the learning process, and to ensure that the optimal solution is obtained within a given time. The inertia of the particles is maintained under the action of inertia weight w, which shows the trend of expanding the search space and has the ability to explore new areas.

In the statistical acceleration term, c₁ and c₂ refer to the acceleration weights to accelerated particles to the current optimal position p_best and the global optimal position g_best. By analyzing the experimental data, it is found that there is an optimal value in the acceleration model under different parameters to guide the particles to move in the specified direction. Without the latter two parts, c₁ = c₂ = 0, the particles will continue to travel at the current speed until they reach the boundary. Due to limited search scope, it will become very difficult to find high-quality solutions. Without the first part, that is, w = 0, the velocity of the particle will only be affected by its current best position p_best and its global best position g_best, while the velocity itself lacks memory.

4. Experimental Results

The establishment of the above model can contribute to the mobilization and stockpiling of emergency medical supplies in public health issues. We set the necessary parameters of the model according to the actual data, which can make the model conform to the development of modern public health issues and widely used in practice and more efficient. This is a great help to the research of emergency material mobilization and stockpiling for future generations.

4.1. Parameter Fitting of the SEIRD Model

In this paper, the unit time is set as day (d). To solve the differential equations, it is necessary to estimate the parameters of the equations. To calculate the development trend of modern public health issues, according to the COVID-19 epidemic report issued by the China Health and Health Commission and the Hubei Health and Health Commission of China, the COVID-19 epidemic data released from 11 January 2020 to 11 April 2020 in the initial stage of the epidemic are used as fitting data, including confirmed data, lurker data, cured data, and death data [42].

It is necessary to preprocess the data before fitting the parameters. In the early stage of the epidemic, the monitoring reagent resources are scarce, the medical staff are insufficient, and the people are not familiar with the illness. Panic occurs easily, leading to hiding the actual number of infected people [43], and large fluctuations in the statistical data in Hubei.

On 27 January 2020, due to the strengthening of detection capabilities, cases that had not been detected before turned into new cases, and there were more newly confirmed cases. Cases were allocated to the first 5 days in proportion. Damir Kopza Sarnov, director of the National Public Health Center of the Ministry of Health of Kazakhstan, was interviewed by reporters on 8 May 2020 and commented on the recent prevention and control of the COVID-19 epidemic in China. According to Kopza Sarnov, the average treatment cycle of confirmed patients in China is 16~17 days. On 12 February 2020, “clinical diagnosis” was added to the classification of case diagnosis in Hubei Province, so that patients can receive standardized treatment according to confirmed cases as early as possible. The number of clinically diagnosed cases was included in the number of confirmed cases, infected but undetected patients and suspected cases were found as much as possible. A total of 13,332 clinically diagnosed confirmed cases were added, and the cases were assigned to the first 16 days in proportion, to preprocess the data and make it more scientific and convenient to study.

According to the relevant literature, the latency time is designed [44] and adjusted according to the actual situation. The parameters values determined are shown in

Table 4. Initial parameter settings for the SEIRD model.

Parameter	Value	Description
$1/\zeta$	6.4	Latent time
N	80,000	Total population

.

According to the initial data on the COVID-19 epidemic released by the China Health and Health Commission and the CDC, using the epidemic data released on 11 January 2020, as input, the coefficients β, γ, and μ of the differential equations are fitted by MATLAB using the least-squares method, and the differential equations are fitted by fourth-order Runge–Kutta. The results of the coefficient fitting are shown in

Table 5. Fitting table of SEIRD model coefficients.

Parameter	Value	Description
β	0.947695770098242	Infection rate
$\gamma$	0.039590527136846	Healing rate
$\mu$	0.001665734397157125	Death rate

, and the simulation diagram is shown in Figure 2.

According to the results of the fitting in Figure 2, it can be seen that the number of susceptible persons fitted by the SEIRD model will gradually decrease, while the number of the exposed will first decrease and then increase. And the number of patients will produce a peak, while the number of recovered persons and dead persons will always increase. The majority of individuals will initially become patients, subsequently recover, and only a small minority are likely to die, owing to China’s effective medical treatment and appropriate policies. The predicted results are consistent with the actual data, and the fitting effect is very consistent with the development of the epidemic situation. According to the China CDC report, as of December 20, 2022, 82.4% of people have suffered from COVID-19 and more than 82% of the population has been infected in two months. Most people will experience a 4–7-day cycle of illness, the virus toxicity will weaken, and most people will recover slowly.

Due to China’s precise prevention and control and adherence to the accurate policy of dynamic clearing, the number of infected and exposed cases has been controlled, and the first aid measures are very timely, greatly reducing the number of people who died from the epidemic in China. At the same time, the epidemic condition is concealed, and some people are ill due to epidemic panic and are not reported. Therefore, there is a small deviation between the fitted data and the actual data, but it is in line with the actual development of the epidemic, so the fitting effect is good.

4.2. Setting of the Demand Urgency Function

In order to obtain an accurate calculation system of the urgency function of the demand, according to the principal component analysis method, the data reports released by the United Nations, the World Health Organization, and the World Bank and the COVID-19 epidemic statistics and policy tracking system released by Johns Hopkins University and Oxford University [45,46]. According to different geographical locations, the data of 10 countries (United States, Canada, Mexico, Britain, Russia, Germany, Philippines, Singapore, Turkey, and Chile) with prominent economies in different continents and more data for studying the prevention and control of public health issues in 2021 are shown in

Table 6. Data of countries in 2021.

State	X1 Population Density	X2 Strict Index of Prevention and Control Policy	X3 Receives Inbound Tourists	X4 Enrollment Rate of Institutions of Higher Learning	X5 Median Age	X6 Vaccination rate	X7 Number of Beds for Thousands of People	X8 GDP Per Capita	X9 Health Expenditure as a Percentage of GDP	X10 Consumer Spending as a Percentage of GDP	X11 UHC Coverage Index
United States	36.84	49.54	22,100,000	54.6	37.7	64.98	3.3	70,248.6	16.9	82.6	86
Canada	4.2	64.95	3,060,000	53.4	40.2	75.84	3.5	51,987.9	8.7	76.2	91
Mexico	64.67	38.89	31,860,000	30.5	29	50.23	3.3	10,045.7	3.3	77.9	75
Britain	277.17	39.97	5,940,000	60.9	39.6	72.44	2.3	46,510.3	9.9	82.8	88
Russia	8.86	54.17	290,000	60.1	38.8	33.41	8.5	12,194.8	5.9	67.8	79
Germany	239.29	34.25	10,320,000	51.5	44.9	69.09	8	51,203.6	11.02	71.4	88
Philippines	379.6	72.58	160,000	28.7	24.5	24.09	3.3	3460.5	3.3	90.8	58
Singapore	8698.48	47.3	330,000	63.8	41.8	83.45	3.8	72,794	3.2	42.5	89
Turkey	110.15	42.45	29,930,000	33.4	30.9	63.21	3.3	9661.2	3.64	68.4	76
Chile	25.89	38.62	190,000	49.6	34.9	79.49	3.3	16,265.1	5.83	75.3	82

. Using SPSS software to perform the analysis of principal components in the data, the correlation matrix is obtained, as shown in

Table 7. Correlation matrix.

	X1	X2	X3	X4	X5	X6	X7	X8	X9	X10	X11
X1	1
X2	−0.02	1
X3	−0.287	−0.41	1
X4	0.394	−0.162	−0.52	1
X5	0.297	−0.346	−0.323	0.875	1
X6	0.373	−0.511	−0.026	0.515	0.622	1
X7	−0.081	−0.101	−0.225	0.275	0.445	−0.285
X8	0.497	−0.123	−0.14	0.709	0.758	0.663	−0.051	1
X9	−0.316	−0.133	0.086	0.445	0.514	0.278	0.082	0.623	1
X10	−0.824	0.273	0.144	−0.461	−0.485	−0.448	−0.257	−0.37	0.328	1
X11	0.256	−0.44	−0.095	0.795	0.901	0.829	0.103	0.783	0.524	−0.441	1

.

It can be seen that the correlation between variables is moderate and that the selected indicators have a suitable level to explain the degree of COVID-19 demand. At the same time, p = 0.001 < 0.01, indicating that the data released by the United Nations and the World Health Organization can effectively reflect the situation of COVID-19, and the data are valid.

At the same time, according to

Table 8. Principal component contribution table.

Composition	Total Variance Explained
	Initial Eigenvalue			Extracting the Sum of Squares of Loads
	Total	Variance Percentage	Cumulative/%	Total	Variance Percentage	Cumulative/%
1	4.978	45.254	45.254	4.978	45.254	45.254
2	2.001	18.189	63.443	2.001	18.189	63.443
3	1.679	15.264	78.707	1.679	15.264	78.707
4	1.281	11.642	90.35
5	0.593	5.389	95.739
6	0.248	2.255	97.995
7	0.158	1.436	99.431
8	0.056	0.507	99.937
9	0.007	0.063	100
10	3.35 × 10−16	3.04 × 10−15	100
11	−1.78 × 10−16	−1.62 × 10−15	100

, the contribution rates of the first, second, third, and fourth principal components are 45.254%, 18.189%, 15.264%, and 11.642%, respectively, and the total contribution rate is as high as 90.35%. According to the general principle of eigenvalue selection, only the first four principal components can be selected to retain the information of the original index, and it is simplified into four new comprehensive indexes, thus achieving an excellent dimension reduction effect, and the cumulative contribution rate is as high as 70~95%. Because the first three indicators have reached 70% of the contribution rate, the fourth principal component contribution is low, so only the first three principal components are studied.

According to the rotated component matrix

Table 9. Composition matrix after rotation.

Indicators	1	2	3
X1		0.905
X2			0.591
X3			−0.809
X4	0.82
X5	0.92
X6	0.755
X7			0.581
X8	0.853
X9	0.711	−0.626
X10		−0.88
X11	0.954

and component matrix

Table 10. Composition matrix table.

Indicators	1	2	3
X1	−0.041	0.41	0.001
X2	−0.108	−0.028	0.355
X3	0.015	−0.075	−0.455
X4	0.164	0.012	0.212
X5	0.198	−0.027	0.131
X6	0.156	0.104	−0.256
X7	0.03	−0.063	0.335
X8	0.186	−0.001	−0.004
X9	0.23	−0.37	0.031
X10	0.01	−0.389	0.023
X11	0.215	−0.02	−0.066

, through the analysis results of the principal components, it can be seen that the enrollment rate of colleges and universities, median age, vaccination rate, per capita GDP, percentage of health expenditure to GDP, and UHC coverage index have a high load on the first factor. These indicators objectively reflect the country’s ability to fight against pneumonia in COVID-19, so they are named “fighting ability”. Population density, the percentage of health expenditure to GDP and the percentage of consumption expenditure to GDP have a high load on the second factor. These indicators objectively reflect the resilience of the country in the face of pneumonia in COVID-19, so they are named “resilience”. The control degree of epidemic prevention policy, the number of inbound tourists received, and the number of beds per thousand people have a high load on the third factor. These indicators reflect the emergency response ability in the face of pneumonia in COVID-19, so they are named “emergency response ability”. The proportion of principal components is set as a. For convenience in calculation and normalization, resistance ability a₁ = 57. 5%, the resilience ability a₂ = 23. 11% and the emergency response ability a₃ = 19. 39%. Set the proportion of indicators as b, b₁₁ = −0. 041, b₁₂ = 0. 41, and so on b_ij.

5. System Simulation Based on Six Cities in Jiangsu Province

5.1. Simulation of the Urgency of Demand in Six Cities in Jiangsu Province

In order to verify the feasibility, real time, and rationality of the model, the model in this paper is simulated. According to different locations (four cities in southern Jiangsu, one city in central Jiangsu, and one city in northern Jiangsu), the data of six cities in Jiangsu Province (Nanjing, Wuxi, Xuzhou, Changzhou, Suzhou, and Nantong) were selected for simulation, and six cities in Jiangsu Province were designed as six demand points. The urgency of the demand of six cities was calculated according to the epidemic data released by Jiangsu Health and Health Commission, Municipal Health and Health Commissions and CDC.

Firstly, the SEIRD model is used to predict the number of infected people. According to the data released by the Jiangsu Provincial Health and Wellness Committee Office, the data released on 1 February 2020 is set as the initial data [47], as shown in

Table 11. Initial epidemic data of six cities in Jiangsu Province.

	Nanjing	Wuxi	Xuzhou	Changzhou	Suzhou	Nantong
S	9.32 million people	7.464 million people	9.084 million people	5.28 million people	12.75 million people	7.728 million people
E	528	255	620	192	571	560
I	33	19	30	15	36	17
R	2	0	0	0	2	0
D	0	0	0	0	0	0

. At this time, the epidemic had just begun to spread and emergency medical materials were in urgent demand.

As emergency medical supplies stored in each city were sufficient in the previous month, the urgency of demand in each city was predicted on the 31st day and emergency medical supplies were dispatched. According to the calculation steps in Section 3.1 of this paper, use MATLAB to write the code, and take the forecast data of the 31st day as shown in

Table 12. Forecast data of six cities in Jiangsu Province on the 31st day (person).

	Nanjing	Wuxi	Xuzhou	Changzhou	Suzhou	Nantong
S	7,258,937	6,369,747	6,810,072	4,455,732	10,436,400	5,772,536
E	1,287,407	693,591	1,411,396	521,551	1,456,982	1,212,793
I	672,290	349,168	748,666	23,719	745,479	644,559
R	97,277	49,414	109,294	37,422	106,613	94,150
D	4093	2079	4598	1574	4846	3961

.

After calculation, the forecast of the demand for emergency medical supplies is obtained on the 31st day: Nanjing-2,881,025.25 kg, Wuxi-2,283,539.1 kg, Xuzhou-2,819,734.2 kg, Changzhou-1,509,471.75 kg, Suzhou-3,919,472.1 kg, and Nantong-2,399,772.75 kg.

Based on Jiangsu Statistical Yearbook-2021 data and the data released by municipal health and health commissions, the urgency of demand Y_1k of epidemic prevention and control ability in each city is Nanjing-0.1861, Wuxi-0.1975, Xuzhou-0.0963, Changzhou-0.1766, Suzhou-0.1854, and Nantong-0.1851, respectively.

Based on the forecast of emergency medical material demand on the 31st day, the emergency medical materials demand urgency Y_2k of each city is Nanjing-0.1822, Wuxi-0.1444, Xuzhou-0.1783, Changzhou-0.0955, Suzhou-0.2479, and Nantong-0.1518, respectively.

When the weights φ₁ and φ₂ in the total demand urgency function are set to 0.3 and 0.7, respectively, the total demand urgency Y_k of each city is calculated and normalized as Nanjing-0.1834, Wuxi-0.1603, Xuzhou-0.1537, Changzhou-0.1198, Suzhou-0.2291, and Nantong-0.1536. At the same time, the ranking of total demand urgency is shown in

Table 13. Table of ranking of the urgency of demand in six cities in Jiangsu Province.

Sort	Demand Points	Demand Urgency
1	Suzhou (Y0)	0.2291
2	Nanjing (Y1)	0.1834
3	Wuxi (Y2)	0.1603
4	Xuzhou (Y3)	0.1537
5	Nantong (Y4)	0.1536
6	Changzhou (Y5)	0.1198

.

It can be seen that in the early stage of the outbreak, according to news reports and data released by the Jiangsu Provincial Health and Health Commission, Suzhou was the first area with the largest outbreak and the most serious epidemic. At this time, the demand in Suzhou demand is the most urgent. Nanjing has Lukou International Airport and is the capital of Jiangsu Province, so the demand urgency is second. Wuxi is near Suzhou City and Shanghai City, and has a large flow of people and economy, so the demand urgency ranks third. Xuzhou City is located in the north of Jiangsu Province, and its economic ability is relatively poor, so its resistance ability is weak, and its demand urgency is fourth. Nantong and Changzhou, both near Suzhou, both have a high ability to fight against epidemic situation, so the demand urgency is low. The data are consistent with reality, and the feasibility and accuracy of the model are high.

5.2. Simulation of the Transportation and Storage of Emergency Medical Materials in Six Cities in Jiangsu Province

The city with the highest urgency of demand is taken as the dispatch point of emergency medical materials, that is, Suzhou is set as Y₀. The map of six cities is shown in Figure 3.

For convenience in the calculation, 50 vehicles are set as a group to meet the total demand of 6 cities. According to relevant references [48] and for this model, the parameters are set as shown in

Table 14. Simulation parameter settings.

Parameter	Content
The earliest service time acceptable to demand point a ETa	0
The last service time acceptable to demand point a RTa	2.5 d
Vehicle model	Large trucks
Number of available vehicles K	5 groups of vehicles
Vehicle speed v0	40 km/h
Vehicle rated weight q0	10 t
The cost per unit distance of vehicle c0	4.5 ¥
The start-up cost of vehicle c1	50 ¥
The penalty cost per unit time o	60 ¥
Service time a	0.5 d

.

Taking Suzhou City, the distribution center, as the origin, establish the coordinates, select points with 25 km as a unit, and obtain the geographical position of each demand point, as shown in

Table 15. Location settings of six cities in Jiangsu province.

Demand Points	X	Y
Suzhou (Y0)	0	0
Nanjing (Y1)	6.8	3.4
Wuxi (Y2)	1	1
Xuzhou (Y3)	12.2	12.9
Nantong (Y4)	−1	3.2
Changzhou (Y5)	2.2	2.2

.

PSO is used to solve the model and Python code is used to compile particle swarm optimization. P₁ and P₂ in the objective function of a single objective are set to 0.4 and 0.6, respectively. To solve the model, PSO is selected and the population number is set at 50, the inertia factor W is set at 0.2, the self-cognition factor C₁ is set at 0.4, the social cognition factor C₂ is set at 0.4 and the iteration times are 1000 times. The data calculated above are inserted into the simulation, and the conclusion is shown in Figure 4.

It can be seen in Figure 4 that three batches of vehicles are used for transportation, the first batch is Suzhou-Nanjing-Suzhou, the second batch is Suzhou-Wuxi-Nantong-Suzhou and the third batch is Suzhou-Xuzhou-Changzhou-Suzhou. At this time, the global optimum is reached. The approximate optimal vehicle distance is 1461.45 km and the total cost is 6726.5 yuan. It proves the feasibility of the model designed in this paper.

If more demand points are established, a more complex roadmap will be produced. In the actual situation, the demand point is often set as the sanitary fixed-point storage warehouse in each district of each city, and the situation of road traffic will be more changeable.

6. Discussion

6.1. Discussion of Experimental Results

This paper presents a new model that can be applied to the mobilization and stockpiling of emergency medical supplies in public health events. The model takes full account of the key considerations for public health events. The model built in this paper completes the work of forecasting the development of public health events, forecasting the demand for emergency supplies, forecasting the degree of urgency mobilizing, and stockpiling emergency supplies considering the degree of urgency and cost. When a public health event occurs again, the model parameters can be modified according to the actual situation of the region in order to complete the response of emergency medical supplies in advance. Furthermore, the model built in this paper can be more widely used, and it has a wide applicability in the problem of mobilization and stockpiling of emergency supplies, such as the emergency mobilization of emergency supplies during earthquake relief, the emergency mobilization of emergency supplies during flooding, etc. The modelling and problem-solving ideas in this paper can be considered to predict the development of the event and the demand for emergency supplies of the affected people in the disaster area in advance, to set the parameters to calculate the urgency of the demand, and then to establish a more scientific scheduling reserve model and to make decisions in a fast and precise manner. It can help to reduce the loss of the disaster area and protect the affected people.

Our model considers multi-objective optimization and the more practical VRPTW problem, as described in the literature review summarized by Liu, X. et al. [49]. Previous researchers have conducted predictive simulations of the occurrence of public health events, while other researchers have investigated the problem of deterministic-based mobilization and stockpiling [50,51]. In the field of emergency management, advance decision making can significantly reduce losses. Therefore, in the field of emergency mobilization and stockpiling research, the study in this paper considers many practical issues and combines the SEIR system dynamics model with the VRPTW problem, which provides assistance in making decisions in advance in emergency management.

This research could be of great help to practitioners in related fields. It is well known that the most dangerous aspect of public health events is their rapid spread. Practitioners can make use of the model built in this paper to carry out emergency medical supplies and stockpiles before the public health event breaks out on a large scale, greatly reducing the probability of dispatchers being infected. In addition, having enough emergency medical supplies can be of great help in suppressing the outbreak of a public health event. Using the model, we built can improve the stockpiling of emergency medical supplies, which in turn can improve the safeguards for healthcare workers and reduce the risk of healthcare workers. Moreover, the models developed in this paper can assist management decision makers in making the right decisions, and having emergency medical supplies at their disposal can greatly reduce the problem of online public opinions, which helps the public’s confidence in the fight against public health events.

6.2. Future Studies

This paper studies public health issues, taking the recent COVID-19 epidemic as the research object, aiming to predict the demand for emergency medical materials and optimize VRPTW. Some aspects of this paper need to be further improved, including the following aspects:

• Mode of transportation and storage of emergency medical materials:

Considering the strong infectivity and high invisibility of the outbreak, we need to further investigate whether there are surplus stocks in medical institutions to allocate emergency medical supplies directly. On this basis, a bi-level programming mathematical model is established, which takes the minimum total transportation cost as the objective function and considers the constraints such as distance between hospitals and transit time. An improved metaheuristic algorithm is designed to solve the problem, and the optimal solution is obtained. In the process of solving the model, the amount of materials left by the vehicle must be fully considered to ensure the accuracy and reliability of the final result;

• Demand forecasting:

Although this paper predicts the number of infected people based on the initial data on the actual epidemic situation in China, there is some subjectivity in the set demand volume of emergency medical materials for various affected people. Furthermore, this article only considers the demand for emergency medical materials, without considering the quantity of other emergency materials, and the types of emergency materials are diverse during the disaster;

• Path planning:

Taking a single logistics distribution center as an example, this paper makes an in-depth study on this VRPTW problem and considers the timeliness of emergency medical materials. To better cope with the actual public health emergency rescue scenario, it is necessary to establish a distribution route optimization model considering the dynamic demand for various emergency materials;

• Solution algorithm:

In this paper, the PSO algorithm is used to solve the approximate optimization model, and the approximate optimal solution of the optimal distribution path is obtained. However, with the in-depth development of algorithms, more metaheuristic algorithms suitable for a specific context will emerge. And the selection of algorithms may produce diversity, so different algorithms should be selected for different contexts;

• Inclusion of new technologies:

There are new technologies that can improve the efficiency of public health incident responses. For example, the use of additive manufacturing (AM) technology has become widespread in recent years, which has been demonstrated that AM can be used as an emergency solution for supply chain (SC) disruptions [52]. AM technology can be very helpful in the recovery and reconstruction of emergency medical supply chains. It helps to increase the resilience of the emergency medical supplies supply chain. These new technologies can greatly improve the efficiency of emergency material mobilization and stockpiling and provide new decision-making options, which could be considered in future research.

7. Countermeasures and Suggestions

7.1. Countermeasures and Suggestions Based on the SEIRD Prediction Model

According to the SEIRD prediction model designed in this paper, if relevant countermeasures can affect the corresponding model parameters, it can effectively reduce the losses caused by public health issues in reality. In this paper, according to the parameters such as “infection rate”, “cure rate”, and “mortality rate” in the SEIRD model and according to the specific situation of epidemic situation, relevant countermeasures and suggestions are put forward:

• Isolation Countermeasures:

People take the countermeasures of self-isolation, and confirmed patients should be isolated in designated places to prevent the spread of viruses, so it can effectively reduce the parameter “infection rate” and prevent a large-scale outbreak of the epidemic. Timely isolation of susceptible persons and confirmed patients can not only reduce the penalty cost and time cost caused by the transportation and storage of emergency medical materials, but also prolong the development of vaccines;

• Vaccination Countermeasures:

Vaccination of susceptible people should be carried out in time. The sooner it starts, the more large-scale group immunity can be generated, and it is more difficult for viruses to invade. It is the vaccination of susceptible people (young people, elderly people, and people with serious diseases) who have a higher “infection rate” and “mortality rate” and can easily become a breakthrough in public health issues;

• Medical Countermeasures:

Medical points in each region should strengthen their ability to cope with public health issues and strengthen the medical level of hospitals, health centers, and other medical units, which can improve the “cure rate” and reduce the “mortality rate”. Through the initial outbreak of pneumonia in COVID-19, Wuhan, it can be seen that medical personnel are susceptible people who come into direct contact with patients, and medical units should strengthen the professional and technical training of medical personnel to reduce the “infection rate” of such people. At the same time, rural areas have poor sanitary conditions and a low medical level, so we should focus on the ability to deal with public health issues in rural areas.

It can be seen that the countermeasures and suggestions obtained according to the model parameters should isolate the virus to the maximum extent, and make people have group immunity as soon as possible, so as to gradually overcome the difficulties of this epidemic. After this epidemic, countries around the world have greatly improved their experience in dealing with and coping with public health issues, which provides help for the possibility of recurrence of public health issues in the future, but we still need to continue to study more effective corresponding ways.

7.2. Countermeasures and Suggestions Based on the Transportation and Reserve Model

The effective transportation and storage of emergency medical materials is the most important means of solving public health issues. When public health emergencies occur, the demand for emergency medical materials will increase directly. According to the transportation and storage model designed in this document, relevant countermeasures and suggestions are presented:

• To predict public health issues at the beginning and grasp the golden time before public health issues broke out, we should focus on strengthening the transportation capacity of emergency medical materials in areas where public health issues occurred, strengthening the manpower and material resources in areas where public health issues occurred in advance, and predict the demand for transportation in advance;
• The emergency medical material transport and reserve network can be established in advance [53], the processing speed of the emergency medical materials transport and reserve can be strengthened, and the public health emergency management center can be established. The urgency of demand for each city demand point can be calculated in advance, the emergency medical material storage center can be set according to the urgency of demand and through prediction and calculation, and the site selection of the emergency medical material storage center can be carried out in advance. When a large-scale public health event occurs, the transportation and storage of emergency medical material can be carried out for the first time, and the emergency medical material storage center should be established in advance for areas with weak transportation capacity and strict transportation conditions, to reduce the injury and transportation cost caused by public health issues;
• It is necessary to adopt a more scientific mode of transport and storage. After completing the construction of the emergency medical materials storage center, the latest unmanned aerial vehicle technology can be used for transportation tasks in areas with high transportation cost and strict transportation conditions. Compared to vehicles, unmanned aerial vehicles have lower cost and more flexible transportation modes and also reduce the spread of public health incidents and virus infection of emergency medical materials caused by floating personnel.

8. Conclusions

This paper focuses on the prediction of the number of people affected by public health issues, the prediction of the demand for emergency medical supplies, and the transportation and storage of emergency medical supplies. Compared to the general logistics system, the core of this paper is to consider the dynamic number of infected people under public health issues and the urgency of emergency medical material demand, and to present the dual goals of weak economy and timeliness of the emergency logistics system, that is, the shortest response time and the lowest delay cost. On this basis, a multistage optimal scheduling model is constructed to realize the decision-making management of emergency medical materials transportation and storage under public health emergencies. By constructing a model and solving it, we can realize the prevention and emergency transportation of public health issues and provide suggestions and theoretical support for the new modern public health issues in the future.

The research results obtained in this paper are mainly reflected in the in-depth exploration and analysis of related fields:

• Continue comprehensive analysis and research of the literature related to emergency logistics:

This paper discusses the connotation of emergency logistics and emergency medical materials and focuses on the solution and application of related algorithms. It summarizes various methods and application scenarios of emergency materials demand prediction and vehicle dispatching optimal path solution based on the SEIR model of infection system dynamics and metaheuristic algorithm;

• Building demand forecasting model:

Forecast the scale of demand for emergency medical supplies at the demand points. First, this paper uses the SEIRD model of system dynamics, uses the least-squares method to fit the parameters of the initial data on the pneumonia epidemic situation in COVID-19, Hubei province, and uses MATLAB to predict the epidemic situation in a certain period in the future. Second, based on the daily consumption of healthy people as a benchmark, this paper defines individual emergency medical materials, and then obtains the daily demand for emergency medical materials from various people, and the total demand for emergency medical materials of demand points by solving;

• Establishing a demand urgency function:

In this paper, considering the dual factors that influence the epidemic prevention and control ability of the demand points and the urgency of the demand for emergency medical materials, the analysis of the principal component of the evaluation index system of the epidemic prevention and control ability is carried out by SPSS, and the urgency function of the demand of the epidemic prevention and control ability is established. Then, the urgency function of the demand for emergency medical materials is established using the predicted demand for emergency medical materials demand. Finally, the total urgency function of demand is designed according to the two designed demand urgency functions;

• Establishing the path optimization model:

In this paper, a vehicle routing optimization model is established, which takes into account the constraints of dual objectives, demand urgency, and time window constraints. With the objective of minimizing the penalty cost for delay and the response time of the system, the vehicle routing optimization model is established combined with the constraints required by the model, and the approximate optimal solution of the model is carried out by using a Python design particle swarm optimization algorithm;

• Simulation example:

This paper combines theory with practice, constructs a distribution network with six nodes in Jiangsu, and simulates it with demand forecasting model and vehicle routing model. Finally, it uses a Python and particle swarm optimization algorithm to solve the model, and draws a conclusion, which scientifically verifies the feasibility of the model and algorithm and provides valuable practical experience for material demand forecasting and vehicle routing arrangement under emergency logistics.