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New Challenges in Mathematical Modelling and Control of COVID-19 Epidemics: Analysis of Non-pharmaceutical Actions and Vaccination Strategies

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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Biology".

Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 26274

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Prof. Dr. Cristiano Maria Verrelli

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Electronic Engineering Department, University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy
Interests: control systems engineering; biosystems engineering; mechatronics control systems; adaptive control
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Fabio Della Rossa

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Diparimtento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Piazza Leonardo da Vinci, 32 20133 Milano, Italy
Interests: dynamical systems; non-linear dynamics; bifurcation theory

Special Issue Information

Dear Colleagues,

Since being officially reported in December 2019 in China, COVID-19 (SARS-CoV-2) immediately reached pandemic proportions throughout six continents and over 210 countries, with the effects on the different age strata of society being highly nonuniform.

Long-term lockdowns were unfeasible and contact-tracing procedures dramatically lost their efficacy at high case numbers. Afterward, the availability of approved COVID-19 vaccines, such as Pfizer/BioNTech, Moderna, Oxford–AstraZeneca AZD1222, and J&J Ad26.COV2.S, has led to mass vaccination rollouts around the world. However, several concerns are being raised given the recent emergence of new COVID-19 variants, which are reported to have increased transmissibility and possibly cause more severe disease compared to the original strain. The potential of such variants for vaccine-induced immunity escape, along with the slightly uncertain duration of vaccine-based immunity, has led to the expectation that vaccination alone will not control the spread of the infection. It is now becoming clear that a carefully planned vaccination campaign (possibly including children as new actors worldwide) needs to be coordinated with continued implementation of nonpharmaceutical interventions, including the alternation of opening and closure phases and public health policy actions to preserve social distancing.

With vaccine efficacy, variants’ actions, age-stratification effects, and the specificity of individual behaviours as potential game-changers, researchers are encouraged to implement new strategies while combining innovative approaches for interpreting current epidemic scenarios and forecasting new ones.

Accordingly, the goal of this Special Issue is to present new results and tools in mathematical modelling (both in the stochastic and the deterministic frames) for the control of epidemics to identify the complex dynamics at the root of this situation.

Relying on the multidisciplinary approach that is typical of complex systems, research papers, communications, and review articles from different mathematical and engineering fields are welcome on the following subtopics:

Analysis of the effects of vaccination strategies by considering the specificity of vaccines and the related immunity duration, age-dependent factors, mechanisms of virus transmission, the specificity of individual behaviours, spatial effects, social networks, and contact patterns.
Analysis of the effects of COVID-19 variants in terms of increased transmissibility and severity of disease, as well as of vaccine-induced immunity escape.
Analysis of the effects of nonpharmaceutical interventions and their relative weight with respect to vaccination strategies in terms of deaths and infections.
Analysis of coordinated actions, including non-pharmaceutical interventions and vaccination
strategies.

Prof. Dr. Cristiano Maria Verrelli
Prof. Dr. Fabio Della Rossa
Guest Editors

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Keywords

COVID-19
SARS-CoV-2
modelling
control
vaccine
virus transmission
spatial effects
contact patterns
variants
immunity
social distancing
nonpharmaceutical actions
age strata
complex dynamics

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Published Papers (12 papers)

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Editorial

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6 pages, 182 KiB

Open AccessEditorial

New Challenges in the Mathematical Modelling and Control of COVID-19 Epidemics: Analysis of Non-Pharmaceutical Actions and Vaccination Strategies

by Cristiano Maria Verrelli and Fabio Della Rossa

Mathematics 2024, 12(9), 1353; https://doi.org/10.3390/math12091353 - 29 Apr 2024

Cited by 1 | Viewed by 1003

Abstract

Following its official appearance in China in December 2019, COVID-19 (SARS-CoV-2) infection immediately reached pandemic proportions on six continents and in over 195 countries [...] Full article

(This article belongs to the Special Issue New Challenges in Mathematical Modelling and Control of COVID-19 Epidemics: Analysis of Non-pharmaceutical Actions and Vaccination Strategies)

Research

Jump to: Editorial

13 pages, 953 KiB

Open AccessArticle

Two-Age-Structured COVID-19 Epidemic Model: Estimation of Virulence Parameters through New Data Incorporation

by Cristiano Maria Verrelli and Fabio Della Rossa

Mathematics 2024, 12(6), 825; https://doi.org/10.3390/math12060825 - 12 Mar 2024

Cited by 1 | Viewed by 1327

Abstract

The COVID-19 epidemic has required countries to implement different containment strategies to limit its spread, like strict or weakened national lockdown rules and the application of age-stratified vaccine prioritization strategies. These interventions have in turn modified the age-dependent patterns of social contacts. In our recent paper, starting from the available age-structured real data at the national level, we identified, for the Italian case, specific virulence parameters for a two-age-structured COVID-19 epidemic compartmental model (under 60, and 60 years and over) in six different diseases transmission scenarios under concurrently adopted feedback interventions. An interpretation of how each external scenario modifies the age-dependent patterns of social contacts and the spread of COVID-19 disease has been accordingly provided. In this paper, which can be viewed as a sequel to the previous one, we mainly apply the same general methodology therein (involving the same dynamic model) to new data covering the three subsequent additional scenarios: (i) a mitigated coordinated intermittent regional action in conjunction with the II vaccination phase; (ii) a super-attenuated coordinated intermittent regional action in conjunction with the II vaccination phase; and (iii) a last step towards normality in conjunction with the start of the III vaccination phase. As a new contribution, we show how meaningful updated information can be drawn out, once the identification of virulence parameters, characterizing the two age groups within the latest three different phases, is successfully carried out. Nevertheless, differently from our previous paper, the global optimization procedure is carried out here with the number of susceptible individuals in each scenario being left free to change, to account for reinfection and immunity due to vaccination. Not only do the slightly different estimates we obtain for the previous scenarios not impact any of the previous considerations (and thus illustrate the robustness of the procedure), but also, and mainly, the new results provide a meaningful picture of the evolution of social behaviors, along with the goodness of strategic interventions. Full article

(This article belongs to the Special Issue New Challenges in Mathematical Modelling and Control of COVID-19 Epidemics: Analysis of Non-pharmaceutical Actions and Vaccination Strategies)

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25 pages, 1035 KiB

Open AccessArticle

Assessing the Impact of Time-Varying Optimal Vaccination and Non-Pharmaceutical Interventions on the Dynamics and Control of COVID-19: A Computational Epidemic Modeling Approach

by Yan Li, Samreen, Laique Zada, Emad A. A. Ismail, Fuad A. Awwad and Ahmed M. Hassan

Mathematics 2023, 11(20), 4253; https://doi.org/10.3390/math11204253 - 11 Oct 2023

Cited by 1 | Viewed by 1396

Abstract

Vaccination strategies remain one of the most effective and feasible preventive measures in combating infectious diseases, particularly during the COVID-19 pandemic. With the passage of time, continuous long-term lockdowns became impractical, and the effectiveness of contact-tracing procedures significantly declined as the number of cases increased. This paper presents a mathematical assessment of the dynamics and prevention of COVID-19, taking into account the constant and time-varying optimal COVID-19 vaccine with multiple doses. We attempt to develop a mathematical model by incorporating compartments with individuals receiving primary, secondary, and booster shots of the COVID-19 vaccine in a basic epidemic model. Initially, the model is rigorously studied in terms of qualitative analysis. The stability analysis and mathematical results are presented to demonstrate that the model is asymptotically stable both locally and globally at the COVID-19-free equilibrium state. We also investigate the impact of multiple vaccinations on the COVID-19 model’s results, revealing that the infection risk can be reduced by administrating the booster vaccine dose to those individuals who already received their first vaccine doses. The existence of backward bifurcation phenomena is studied. A sensitivity analysis is carried out to determine the most sensitive parameter on the disease incidence. Furthermore, we developed a control model by introducing time-varying controls to suggest the optimal strategy for disease minimization. These controls are isolation, multiple vaccine efficacy, and reduction in the probability that different vaccine doses do not develop antibodies against the original virus. The existence and numerical solution to the COVID-19 control problem are presented. A detailed simulation is illustrated demonstrating the population-level impact of the constant and time-varying optimal controls on disease eradication. Using the novel concept of human awareness and several vaccination doses, the elimination of COVID-19 infections could be significantly enhanced. Full article

(This article belongs to the Special Issue New Challenges in Mathematical Modelling and Control of COVID-19 Epidemics: Analysis of Non-pharmaceutical Actions and Vaccination Strategies)

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16 pages, 500 KiB

Open AccessFeature PaperArticle

Cumulative Incidence Functions for Competing Risks Survival Data from Subjects with COVID-19

by Mohammad Anamul Haque and Giuliana Cortese

Mathematics 2023, 11(17), 3772; https://doi.org/10.3390/math11173772 - 2 Sep 2023

Cited by 1 | Viewed by 3289

Abstract

Competing risks survival analysis is used to answer questions about the time to occurrence of events with the extension of multiple causes of failure. Studies that investigate how clinical features and risk factors of COVID-19 are associated with the survival of patients in the presence of competing risks (CRs) are limited. The main objective of this paper is, under a CRs setting, to estimate the Cumulative Incidence Function (CIF) of COVID-19 death, the CIF of other-causes death, and the probability of being cured in subjects with COVID-19, who have been under observation from the date of symptoms to the date of death or exit from the study because they are cured. In particular, we compared the non-parametric estimator of the CIF based on the naive technique of Kaplan–Meier (K–M) with the Aalen–Johansen estimator based on the cause-specific approach. Moreover, we compared two of the most popular regression approaches for CRs data: the cause-specific hazard (CSH) and the sub-distribution hazard (SDH) approaches. A clear overestimation of the CIF function over time was observed under the K–M estimation technique. Moreover, exposure to asthma, diabetes, obesity, older age, male sex, black and indigenous races, absence of flu vaccine, admission to the ICU, and the presence of other risk factors, such as immunosuppression and chronic kidney, neurological, liver, and lung diseases, significantly increased the probability of COVID-19 death. The highest hazard ratio of

2.03

was observed for subjects with an age greater than 70 years compared with subjects aged 50–60 years. The SDH approach showed slightly higher survival probabilities compared with the CSH approach. An important foundation for producing precise individualized predictions was provided by the competing risks regression models discussed in this paper. This foundation allowed us, in general, to more realistically model complex data, such as the COVID-19 data, and can be used, for instance, by many modern statistical learning and personalized medicine techniques to obtain more accurate conclusions. Full article

(This article belongs to the Special Issue New Challenges in Mathematical Modelling and Control of COVID-19 Epidemics: Analysis of Non-pharmaceutical Actions and Vaccination Strategies)

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26 pages, 3674 KiB

Open AccessArticle

Differential and Time-Discrete SEIRS Models with Vaccination: Local Stability, Validation and Sensitivity Analysis Using Bulgarian COVID-19 Data

by Svetozar Margenov, Nedyu Popivanov, Iva Ugrinova and Tsvetan Hristov

Mathematics 2023, 11(10), 2238; https://doi.org/10.3390/math11102238 - 10 May 2023

Cited by 2 | Viewed by 2164

Abstract

Bulgaria has the lowest COVID-19 vaccination rate in the European Union and the second-highest COVID-19 mortality rate in the world. That is why we think it is important better to understand the reason for this situation and to analyse the development of the disease over time. In this paper, an extended time-dependent SEIRS model SEIRS-VB is used to investigate the long-term behaviour of the COVID-19 epidemic. This model includes vaccination and vital dynamics. To apply the SEIRS-VB model some numerical simulation tools have been developed and for this reason a family of time-discrete variants are introduced. Suitable inverse problems for the identification of parameters in discrete models are solved. A methodology is proposed for selecting a discrete model from the constructed family, which has the closest parameter values to these in the differential SEIRS-VB model. To validate the studied models, Bulgarian COVID-19 data are used. To obtain all these results for the discrete models a mathematical analysis is carried out to illustrate some biological properties of the differential model SEIRS-VB, such as the non-negativity, boundedness, existence, and uniqueness. Using the next-generation method, the basic reproduction number associated with the model in the autonomous case is defined. The local stability of the disease-free equilibrium point is studied. Finally, a sensitivity analysis of the basic reproduction number is performed. Full article

(This article belongs to the Special Issue New Challenges in Mathematical Modelling and Control of COVID-19 Epidemics: Analysis of Non-pharmaceutical Actions and Vaccination Strategies)

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30 pages, 2405 KiB

Open AccessArticle

Advancing COVID-19 Understanding: Simulating Omicron Variant Spread Using Fractional-Order Models and Haar Wavelet Collocation

by Zehba Raizah and Rahat Zarin

Mathematics 2023, 11(8), 1925; https://doi.org/10.3390/math11081925 - 19 Apr 2023

Cited by 4 | Viewed by 2797

Abstract

This study presents a novel approach for simulating the spread of the Omicron variant of the SARS-CoV-2 virus using fractional-order COVID-19 models and the Haar wavelet collocation method. The proposed model considers various factors that affect virus transmission, while the Haar wavelet collocation method provides an efficient and accurate solution for the fractional derivatives used in the model. This study analyzes the impact of the Omicron variant and provides valuable insights into its transmission dynamics, which can inform public health policies and strategies that are aimed at controlling its spread. Additionally, this study’s findings represent a significant step forward in understanding the COVID-19 pandemic and its evolving variants. The results of the simulation showcase the effectiveness of the proposed method and demonstrate its potential to advance the field of COVID-19 research. The COVID epidemic model is reformulated by using fractional derivatives in the Caputo sense. The existence and uniqueness of the proposed model are illustrated in the model, taking into account some results of fixed point theory. The stability analysis for the system is established by incorporating the Hyers–Ulam method. For numerical treatment and simulations, we apply the Haar wavelet collocation method. The parameter estimation for the recorded COVID-19 cases in Pakistan from 23 June 2022 to 23 August 2022 is presented. Full article

(This article belongs to the Special Issue New Challenges in Mathematical Modelling and Control of COVID-19 Epidemics: Analysis of Non-pharmaceutical Actions and Vaccination Strategies)

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19 pages, 744 KiB

Open AccessArticle

On the Impact of Quarantine Policies and Recurrence Rate in Epidemic Spreading Using a Spatial Agent-Based Model

by Alexandru Topîrceanu

Mathematics 2023, 11(6), 1336; https://doi.org/10.3390/math11061336 - 9 Mar 2023

Cited by 3 | Viewed by 1660

Abstract

Pandemic outbreaks often determine swift global reaction, proven by for example the more recent COVID-19, H1N1, Ebola, or SARS outbreaks. Therefore, policy makers now rely more than ever on computational tools to establish various protection policies, including contact tracing, quarantine, regional or national lockdowns, and vaccination strategies. In support of this, we introduce a novel agent-based simulation framework based on: (i) unique mobility patterns for agents between their home location and a point of interest, and (ii) the augmented SICARQD epidemic model. Our numerical simulation results provide a qualitative assessment of how quarantine policies and the patient recurrence rate impact the society in terms of the infected population ratio. We investigate three possible quarantine policies (proactive, reactive, and no quarantine), a variable quarantine restrictiveness (0–100%), respectively, and three recurrence scenarios (short, long, and no recurrence). Overall, our results show that the proactive quarantine in correlation to a higher quarantine ratio (i.e., stricter quarantine policy) triggers a phase transition reducing the total infected population by over 90% compared to the reactive quarantine. The timing of imposing quarantine is also paramount, as a proactive quarantine policy can reduce the peak infected ratio by over

\times 2

times compared to a reactive quarantine, and by over

\times 3

times compared to no quarantine. Our framework can also reproduce the impactful subsequent epidemic waves, as observed during the COVID-19 pandemic, according to the adopted recurrence scenario. The suggested solution against residual infection hotspots is mobility reduction and proactive quarantine policies. In the end, we propose several nonpharmaceutical guidelines with direct applicability by global policy makers. Full article

(This article belongs to the Special Issue New Challenges in Mathematical Modelling and Control of COVID-19 Epidemics: Analysis of Non-pharmaceutical Actions and Vaccination Strategies)

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15 pages, 334 KiB

Open AccessArticle

A New COVID-19 Pandemic Model including the Compartment of Vaccinated Individuals: Global Stability of the Disease-Free Fixed Point

by Isra Al-Shbeil, Noureddine Djenina, Ali Jaradat, Abdallah Al-Husban, Adel Ouannas and Giuseppe Grassi

Mathematics 2023, 11(3), 576; https://doi.org/10.3390/math11030576 - 21 Jan 2023

Cited by 11 | Viewed by 2033

Abstract

Owing to the COVID-19 pandemic, which broke out in December 2019 and is still disrupting human life across the world, attention has been recently focused on the study of epidemic mathematical models able to describe the spread of the disease. The number of people who have received vaccinations is a new state variable in the COVID-19 model that this paper introduces to further the discussion of the subject. The study demonstrates that the proposed compartment model, which is described by differential equations of integer order, has two fixed points, a disease-free fixed point and an endemic fixed point. The global stability of the disease-free fixed point is guaranteed by a new theorem that is proven. This implies the disappearance of the pandemic, provided that an inequality involving the vaccination rate is satisfied. Finally, simulation results are carried out, with the aim of highlighting the usefulness of the conceived COVID-19 compartment model. Full article

(This article belongs to the Special Issue New Challenges in Mathematical Modelling and Control of COVID-19 Epidemics: Analysis of Non-pharmaceutical Actions and Vaccination Strategies)

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18 pages, 15453 KiB

Open AccessArticle

Forecasting a New Type of Virus Spread: A Case Study of COVID-19 with Stochastic Parameters

by Victor Zakharov, Yulia Balykina, Igor Ilin and Andrea Tick

Mathematics 2022, 10(20), 3725; https://doi.org/10.3390/math10203725 - 11 Oct 2022

Cited by 8 | Viewed by 1946

Abstract

The consideration of infectious diseases from a mathematical point of view can reveal possible options for epidemic control and fighting the spread of infection. However, predicting and modeling the spread of a new, previously unexplored virus is still difficult. The present paper examines the possibility of using a new approach to predicting the statistical indicators of the epidemic of a new type of virus based on the example of COVID-19. The important result of the study is the description of the principle of dynamic balance of epidemiological processes, which has not been previously used by other researchers for epidemic modeling. The new approach is also based on solving the problem of predicting the future dynamics of precisely random values of model parameters, which is used for defining the future values of the total number of: cases (C); recovered and dead (R); and active cases (I). Intelligent heuristic algorithms are proposed for calculating the future trajectories of stochastic parameters, which are called the percentage increase in the total number of confirmed cases of the disease and the dynamic characteristics of epidemiological processes. Examples are given of the application of the proposed approach for making forecasts of the considered indicators of the COVID-19 epidemic, in Russia and European countries, during the first wave of the epidemic. Full article

(This article belongs to the Special Issue New Challenges in Mathematical Modelling and Control of COVID-19 Epidemics: Analysis of Non-pharmaceutical Actions and Vaccination Strategies)

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18 pages, 2224 KiB

Open AccessArticle

Growth Recovery and COVID-19 Pandemic Model: Comparative Analysis for Selected Emerging Economies

by Askar Akaev, Alexander I. Zvyagintsev, Askar Sarygulov, Tessaleno Devezas, Andrea Tick and Yuri Ichkitidze

Mathematics 2022, 10(19), 3654; https://doi.org/10.3390/math10193654 - 5 Oct 2022

Cited by 3 | Viewed by 2081

Abstract

The outburst of the COVID-19 pandemic and its rapid spread throughout the world in 2020 shed a new light on mathematic models describing the nature of epidemics. However, as the pandemic shocked economies to a much greater extent than earlier epidemics, the recovery potential of economies was emphasized and its inclusion in epidemic models is becoming more important. The present paper deals with the issues of modeling the recovery of economic systems that have undergone severe medical shocks, such as COVID-19. The proposed mathematical model considers the close relationship between the dynamics of pandemics and economic development. This distinguishes it from purely “medical” models, which are used exclusively to study the dynamics of the spread of the COVID-19 pandemic. Unlike standard SIR models, the present approach involves the introduction of the “vaccine” equation to the SIR model and introduces correction components that include the possibility of re-infection and other nuances such as the number of people at risk of infection (not sick with COVID but not vaccinated); sick with COVID; recovered; fully vaccinated (two doses) citizens; the rate of COVID infection; the rate of recovery of infected individuals; the vaccination coefficients, respectively, for those who have not been ill and recovered from COVID; the coefficient of revaccination; the COVID re-infection rate; and the population fluctuation coefficient, which takes into account the effect of population change as a result of births and deaths and due to the departure and return of citizens. The present model contains governance so that it not only generates scenario projections but also models specific governance measures as well to include the pandemic and restore economic growth. The model also adds management issues, so that it not only generates scenario forecasts but simultaneously models specific management measures as well, aiming to suppress the pandemic and restoring economic growth. The model was implemented on specific data on the dynamics of the spread of the COVID-19 pandemic in selected developing economies. Full article

(This article belongs to the Special Issue New Challenges in Mathematical Modelling and Control of COVID-19 Epidemics: Analysis of Non-pharmaceutical Actions and Vaccination Strategies)

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26 pages, 745 KiB

Open AccessArticle

On Predictive Modeling Using a New Flexible Weibull Distribution and Machine Learning Approach: Analyzing the COVID-19 Data

by Zubair Ahmad, Zahra Almaspoor, Faridoon Khan and Mahmoud El-Morshedy

Mathematics 2022, 10(11), 1792; https://doi.org/10.3390/math10111792 - 24 May 2022

Cited by 25 | Viewed by 2342

Abstract

Predicting and modeling time-to-events data is a crucial and interesting research area. For modeling and predicting such types of data, numerous statistical models have been suggested and implemented. This study introduces a new statistical model, namely, a new modified flexible Weibull extension (NMFWE) distribution for modeling the mortality rate of COVID-19 patients. The introduced model is obtained by modifying the flexible Weibull extension model. The maximum likelihood estimators of the NMFWE model are obtained. The evaluation of the estimators of the NMFWE model is assessed in a simulation study. The flexibility and applicability of the NMFWE model are established by taking two datasets representing the mortality rates of COVID-19-infected persons in Mexico and Canada. For predictive modeling, we consider two pure statistical models and two machine learning (ML) algorithms. The pure statistical models include the autoregressive moving average (ARMA) and non-parametric autoregressive moving average (NP-ARMA), and the ML algorithms include neural network autoregression (NNAR) and support vector regression (SVR). To evaluate their forecasting performance, three standard measures of accuracy, namely, root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) are calculated. The findings demonstrate that ML algorithms are very effective at predicting the mortality rate data. Full article

(This article belongs to the Special Issue New Challenges in Mathematical Modelling and Control of COVID-19 Epidemics: Analysis of Non-pharmaceutical Actions and Vaccination Strategies)

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12 pages, 480 KiB

Open AccessArticle

Two-Age-Structured COVID-19 Epidemic Model: Estimation of Virulence Parameters to Interpret Effects of National and Regional Feedback Interventions and Vaccination

by Cristiano Maria Verrelli and Fabio Della Rossa

Mathematics 2021, 9(19), 2414; https://doi.org/10.3390/math9192414 - 28 Sep 2021

Cited by 7 | Viewed by 2350

Abstract

The COVID-19 epidemic has recently led in Italy to the implementation of different external strategies in order to limit the spread of the disease in response to its transmission rate: strict national lockdown rules, followed first by a weakening of the social distancing and contact reduction feedback interventions and finally the implementation of coordinated intermittent regional actions, up to the application, in this last context, of an age-stratified vaccine prioritization strategy. This paper originally aims at identifying, starting from the available age-structured real data at the national level during the specific aforementioned scenarios, external-scenario-dependent sets of virulence parameters for a two-age-structured COVID-19 epidemic compartmental model, in order to provide an interpretation of how each external scenario modifies the age-dependent patterns of social contacts and the spread of COVID-19. Full article

(This article belongs to the Special Issue New Challenges in Mathematical Modelling and Control of COVID-19 Epidemics: Analysis of Non-pharmaceutical Actions and Vaccination Strategies)

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