Search

Purpose: The ongoing COVID-19 pandemic imposes serious short-term and long-term health costs on populations. Restrictive government policy measures decrease the risks of infection, but produce similarly serious social, mental health, and economic problems. Citizens have varying preferences about the desirability of restrictive policies, and governments are thus forced to navigate this tension in making pandemic policy. This paper analyses the situation facing government using a game-theoretic epidemiological model., Methodology: We classify individuals into health-centered individuals and freedom-centered individuals to capture the heterogeneous preferences of citizens. We first use the extended Susceptible-Exposed-Asymptomatic-Infectious-Recovered (SEAIR) model (adding individual preferences) and the signaling game model (adding government) to analyze the strategic situation against the backdrop of a realistic model of COVID-19 infection., Findings: We find the following: 1. There exists two pooling equilibria. When health-centered and freedom-centered individuals send anti-epidemic signals, the government will adopt strict restrictive policies under budget surplus or balance. When health-centered and freedom-centered individuals send freedom signals, the government chooses not to implement restrictive policies. 2. When governments choose not to impose restrictions, the extinction of an epidemic depends on whether it has a high infection transmission rate; when the government chooses to implement non-pharmacological interventions (NPIs), whether an epidemic will disappear depends on how strict the government's restrictions are., Originality/value: Based on the existing literature, we add individual preferences and put the government into the game as a player. Our research extends the current form of combining epidemiology and game theory. By using both we get a more realistic understanding of the spread of the virus and combine that with a richer understanding of the strategic social dynamics enabled by game theoretic analysis. Our findings have important implications for public management and government decision-making in the context of COVID-19 and for potential future public health emergencies., (© 2023 Elsevier Inc. All rights reserved.)

A new contagious disease or unidentified COVID-19 variants could provoke a new collapse in the global economy. Under such conditions, companies, factories, and organizations must adopt reopening policies that allow their operations to reduce economic effects. Effective reopening policies should be designed using mathematical models that emulate infection chains through individual interactions. In contrast to other modeling approaches, agent-based schemes represent a computational paradigm used to characterize the person-to-person interactions of individuals inside a system, providing accurate simulation results. To evaluate the optimal conditions for a reopening policy, authorities and decision-makers need to conduct an extensive number of simulations manually, with a high possibility of losing information and important details. For this reason, the integration of optimization and simulation of reopening policies could automatically find the realistic scenario under which the lowest risk of infection was attained. In this paper, the metaheuristic technique of the Whale Optimization Algorithm is used to find the solution with the minimal transmission risk produced by an agent-based model that emulates a hypothetical re-opening context. Our scheme finds the optimal results of different generical activation scenarios. The experimental results indicate that our approach delivers practical knowledge and essential estimations for identifying optimal re-opening strategies with the lowest transmission risk., Competing Interests: None., (© 2023 Elsevier Inc. All rights reserved.)

In this paper, a reaction-diffusion COVID-19 model is proposed to explore how vaccination-isolation strategies affect the development of the epidemic. First, the basic dynamical properties of the system are explored. Then, the system's asymptotic distributions of endemic equilibrium under different conditions are studied. Further, the global sensitivity analysis of R 0 is implemented with the aim of determining the sensitivity for these parameters. In addition, the optimal vaccination-isolation strategy based on the optimal path is proposed. Meantime, social cost C ( m , σ ) , social benefit B ( m , σ ) , threshold R 0 ( m , σ ) three objective optimization problem based on vaccination-isolation strategy is explored, and the maximum social cost ( M S C ) and maximum social benefit ( M S B ) are obtained. Finally, the instance prediction of the Lhasa epidemic in China on August 7, 2022, is made by using the piecewise infection rates β 1 ( t ) , β 2 ( t ) , and some key indicators are obtained as follows: (1) The basic reproduction numbers of each stage in Lhasa, China are R 0 ( 1 : 8 ) = 0.4678 , R 0 ( 9 : 20 ) = 2.7655 , R 0 ( 21 : 30 ) = 0.3810 and R 0 ( 31 : 100 ) = 0.7819 ; (2) The daily new cases of this epidemic will peak at 43 on the 20th day (August 26, 2022); (3) The cumulative cases in Lhasa, China will reach about 640 and be cleared about the 80th day (October 28, 2022). Our research will contribute to winning the war on epidemic prevention and control., (© 2023 Elsevier Inc. All rights reserved.)

The effectiveness of control interventions against COVID-19 is threatened by the emergence of SARS-CoV-2 variants of concern. We present a mathematical model for studying the transmission dynamics of two of these variants (Delta and Omicron) in the United States, in the presence of vaccination, treatment of individuals with clinical symptoms of the disease and the use of face masks. The model is parameterized and cross-validated using observed daily case data for COVID-19 in the United States for the period from November 2021 (when Omicron first emerged) to March 2022. Rigorous qualitative analysis of the model shows that the disease-free equilibrium of the model is locally-asymptotically stable when the control reproduction number of the model (denoted by R c ) is less than one. This equilibrium is shown to be globally-asymptotically stable for a special case of the model, where disease-induced mortality is negligible and both vaccine-derived immunity in fully-vaccinated individuals and natural immunity do not wane, when the associated reproduction number is less than one. The epidemiological implication of the latter result is that the combined vaccination-boosting strategy can lead to the elimination of the pandemic if its implementation can bring (and maintain) the associated reproduction number to a value less than one. An analytical expression for the vaccine-derived herd immunity threshold is derived. Using this expression, together with the baseline values of the parameters of the parameterized model, we showed that the vaccine-derived herd immunity can be achieved in the United States (so that the pandemic will be eliminated) if at least 68 % of the population is fully-vaccinated with two of the three vaccines approved for use in the United States (Pfizer or Moderna vaccine). Furthermore, this study showed (as of the time of writing in March 2022) that the control reproduction number of the Omicron variant was approximately 3.5 times that of the Delta variant (the reproduction of the latter is computed to be ≈ 0.2782 ), indicating that Delta had practically died out and that Omicron has competitively-excluded Delta (to become the predominant variant in the United States). Based on our analysis and parameterization at the time of writing of this paper (March 2022), our study suggests that SARS-CoV-2 elimination is feasible by June 2022 if the current baseline level of the coverage of fully-vaccinated individuals is increased by about 20 % . The prospect of pandemic elimination is significantly improved if vaccination is combined with a face mask strategy that prioritizes moderately effective and high-quality masks. Having a high percentage of the populace wearing the moderately-effective surgical mask is more beneficial to the community than having low percentage of the populace wearing the highly-effective N95 masks. We showed that waning natural and vaccine-derived immunity (if considered individually) offer marginal impact on disease burden, except for the case when they wane at a much faster rate (e.g., within three months), in comparison to the baseline (estimated to be within 9 months to a year). Treatment of symptomatic individuals has marginal effect in reducing daily cases of SARS-CoV-2, in comparison to the baseline, but it has significant impact in reducing daily hospitalizations. Furthermore, while treatment significantly reduces daily hospitalizations (and, consequently, deaths), the prospects of COVID-19 elimination in the United States are significantly enhanced if investments in control resources are focused on mask usage and vaccination rather than on treatment., Competing Interests: The author(s) declare no competing interests., (© 2022 Elsevier Inc. All rights reserved.)

This paper presents a bi-level blood supply chain network under uncertainty during the COVID-19 pandemic outbreak using a Stackelberg game theory technique. A new two-phase bi-level mixed-integer linear programming model is developed in which the total costs are minimized and the utility of donors is maximized. To cope with the uncertain nature of some of the input parameters, a novel mixed possibilistic-robust-fuzzy programming approach is developed. The data from a real case study is utilized to show the applicability and efficiency of the proposed model. Finally, some sensitivity analyses are performed on the important parameters and some managerial insights are suggested., (© 2022 Elsevier Inc. All rights reserved.)

Contact Tracing (CT) is one of the measures taken by government and health officials to reduce the spread of the novel coronavirus. In this paper, we investigate its efficacy by developing a compartmental model for assessing its impact on mitigating the spread of the virus. We describe the impact on the reproduction number R 0 of COVID-19. In particular, we discuss the importance and relevance of parameters of the model such as the number of reported cases, effectiveness of tracking and monitoring policy, and the transmission rates to contact tracing. We describe the terms "perfect tracking", "perfect monitoring" and "perfect reporting" to indicate that traced contacts will be tracked while incubating, tracked contacts are efficiently monitored so that they do not cause secondary infections, and all infected persons are reported, respectively. We consider three special scenarios: (1) perfect monitoring and perfect tracking of contacts of a reported case, (2) perfect reporting of cases and perfect monitoring of tracked reported cases and (3) perfect reporting and perfect tracking of contacts of reported cases. Furthermore, we gave a lower bound on the proportion of contacts to be traced to ensure that the effective reproduction, R c , is below one and describe R c in terms of observable quantities such as the proportion of reported and traced cases. Model simulations using the COVID-19 data obtained from John Hopkins University for some selected states in the US suggest that even late intervention of CT may reasonably reduce the transmission of COVID-19 and reduce peak hospitalizations and deaths. In particular, our findings suggest that effective monitoring policy of tracked cases and tracking of traced contacts while incubating are more crucial than tracing more contacts. The use of CT coupled with other measures such as social distancing, use of face mask, self-isolation or quarantine and lockdowns will greatly reduce the spread of the epidemic as well as peak hospitalizations and total deaths.

The storage and distribution of medical supplies are important parts of epidemic prevention and control. This paper first proposes a new nonsmooth two-stage stochastic equilibrium model of medical supplies in epidemic management. The first stage addresses the storage in the pre-disaster phase, and the second stage focuses on the dynamic distribution by enrolling competitions among multiple hospitals over a period of time in the post-disaster phase. The uncertainties are the numbers of infected people treated in multiple hospitals during the period of time, which are time-varying around a nominal distribution predicted by historical experience. The two-stage stochastic equilibrium model is further approximated and transformed to a monotone two-stage stochastic variational inequality (SVI) model that is computationally tractable, with the aid of a smooth approximation technique. We employ the progressive hedging method (PHM) to solve a case study in the city of Wuhan in China suffered from the COVID-19 pandemic. Numerical results are presented to demonstrate the effectiveness of the proposed model in planning the storage and dynamic distribution of medical supplies in epidemic management., (© 2021 Elsevier Inc. All rights reserved.)

The global impact of corona virus (COVID-19) has been profound, and the public health threat it represents is the most serious seen in a respiratory virus since the 1918 influenza A(H1N1) pandemic. In this paper, we have focused on reviewing the results of epidemiological modelling especially the fractional epidemic model and summarized different types of fractional epidemic models including fractional Susceptible-Infective-Recovered (SIR), Susceptible-Exposed-Infective-Recovered (SEIR), Susceptible-Exposed-Infective-Asymptomatic-Recovered (SEIAR) models and so on. Furthermore, we propose a general fractional SEIAR model in the case of single-term and multi-term fractional differential equations. A feasible and reliable parameter estimation method based on modified hybrid Nelder-Mead simplex search and particle swarm optimisation is also presented to fit the real data using fractional SEIAR model. The effective methods to solve the fractional epidemic models we introduced construct a simple and effective analytical technique that can be easily extended and applied to other fractional models, and can help guide the concerned bodies in preventing or controlling, even predicting the infectious disease outbreaks., (© 2021 Elsevier Inc. All rights reserved.)

COVID-19 pandemic has impacted people all across the world. As a result, there has been a collective effort to monitor, predict, and control the spread of this disease. Among this effort is the development of mathematical models that could capture accurately the available data and simulate closely the futuristic scenarios. In this paper, a fractional-order memory-dependent model for simulating the spread of COVID-19 is proposed. In this model, the impact of governmental interventions and public perception are incorporated as part of the nonlinear time-varying transmission rate. In addition, an algorithm for approximating the optimal values of the fractional order and strength of governmental interventions is provided. This approach makes our model suitable for capturing the given data set and consequently reliable for future predictions. The model simulation is performed using the two-step generalized exponential time-differencing method and tested for data from Mainland China, Italy, Saudi Arabia and Brazil. The simulation results demonstrate that the fractional order model calibrates to the data better than its integer order counterpart. This observation is further endorsed by the calculated error metrics., (© 2021 Elsevier Inc. All rights reserved.)

In this paper, a stochastic and a deterministic SIS epidemic model with isolation and varying total population size are proposed. For the deterministic model, we establish the threshold R 0 . When R 0 is less than 1, the disease-free equilibrium is globally stable, which means the disease will die out. While R 0 is greater than 1, the endemic equilibrium is globally stable, which implies that the disease will spread. Moreover, there is a critical isolation rate δ *, when the isolation rate is greater than it, the disease will be eliminated. For the stochastic model, we also present its threshold R 0 s . When R 0 s is less than 1, the disease will disappear with probability one. While R 0 s is greater than 1, the disease will persist. We find that stochastic perturbation of the transmission rate (or the valid contact coefficient) can help to reduce the spread of the disease. That is, compared with stochastic model, the deterministic epidemic model overestimates the spread capacity of disease. We further find that there exists a critical the stochastic perturbation intensity of the transmission rate σ *, when the stochastic perturbation intensity of the transmission rate is bigger than it, the disease will disappear. At last, we apply our theories to a realistic disease, pneumococcus amongst homosexuals, carry out numerical simulations and obtain the empirical probability density under different parameter values. The critical isolation rate δ * is presented. When the isolation rate δ is greater than δ *, the pneumococcus amongst will be eliminated., (© 2020 Elsevier Inc. All rights reserved.)

In this paper, we investigate the effects of the latent period on the dynamics of infectious disease with an imperfect vaccine. We assume a general incidence rate function with a non-monotonicity property to interpret the psychological effect in the susceptible population when the number of infectious individuals increases. After we propose the model, we provide the well-posedness property by verifying the non-negativity and boundedness of the models solutions. Then, we calculate the effective reproduction number R E . The threshold dynamics of the system is obtained with respect to R E . We discuss the global stability of the disease-free equilibrium when R E < 1 and explore the system persistence when R E > 1 . Moreover, we prove the coexistence of an endemic equilibrium when the system persists. Then, we discuss the critical vaccination coverage rate that is required to eliminate the disease. Numerical simulations are provided to: (i) implement a case study regarding the measles disease transmission in the United States from 1963 to 2016; (ii) study the local and global sensitivity of R E with respect to the model parameters; (iii) discuss the stability of endemic equilibrium; and (iv) explore the sensitivity of the proposed model solutions with respect to the main parameters., (© 2020 Elsevier Inc. All rights reserved.)

The 2019 novel coronavirus (COVID-19) emerged at the end of 2019 has a great impact on China and all over the world. The transmission mechanism of COVID-19 is still unclear. Except for the initial status and the imported cases, the isolation measures and the medical treatments of the infected patients have essential influences on the spread of COVID-19. In this paper, we establish a mathematical model for COVID-19 transmission involving the interactive effect of various factors for the infected people, including imported cases, isolating rate, diagnostic rate, recovery rate and also the mortality rate. Under the assumption that the random incubation period, the cure period and the diagnosis period are subject to the Weibull distribution, the quantity of daily existing infected people is finally governed by a linear integral-differential equation with convolution kernel. Based on the asymptotic behavior and the quantitative analysis on the model, we rigorously prove that, for limited external input patients, both the quantity of infected patients and its variation ratio will finally tend to zero, if the infected patients are sufficiently isolated or the infection rate is small enough. Finally, numerical performances for the proposed model as well as the comparisons between our simulations and the clinical data of the city Wuhan and Italy are demonstrated, showing the validity of our model with suitably specified model parameters., (© 2020 Elsevier Inc. All rights reserved.)

In this paper, a multi-scale mathematical model for environmentally transmitted diseases is proposed which couples the pathogen-immune interaction inside the human body with the disease transmission at the population level. The model is based on the nested approach that incorporates the infection-age-structured immunological dynamics into an epidemiological system structured by the chronological time, the infection age and the vaccination age. We conduct detailed analysis for both the within-host and between-host disease dynamics. Particularly, we derive the basic reproduction number R 0 for the between-host model and prove the uniform persistence of the system. Furthermore, using carefully constructed Lyapunov functions, we establish threshold-type results regarding the global dynamics of the between-host system: the disease-free equilibrium is globally asymptotically stable when R 0 < 1, and the endemic equilibrium is globally asymptotically stable when R 0 > 1. We explore the connection between the within-host and between-host dynamics through both mathematical analysis and numerical simulation. We show that the pathogen load and immune strength at the individual level contribute to the disease transmission and spread at the population level. We also find that, although the between-host transmission risk correlates positively with the within-host pathogen load, there is no simple monotonic relationship between the disease prevalence and the individual pathogen load.

In this paper, we propose and analyze a nonautonomous predator-prey model with disease in prey, and a discrete time delay for the incubation period in disease transmission. Employing the theory of differential inequalities, we find sufficient conditions for the permanence of the system. Further, we use Lyapunov's functional method to obtain sufficient conditions for global asymptotic stability of the system. We observe that the permanence of the system is unaffected due to presence of incubation delay. However, incubation delay affects the global stability of the positive periodic solution of the system. To reinforce the analytical results and to get more insight into the system's behavior, we perform some numerical simulations of the autonomous and nonautonomous systems with and without time delay. We observe that for the gradual increase in the magnitude of incubation delay, the autonomous system develops limit cycle oscillation through a Hopf-bifurcation while the corresponding nonautonomous system shows chaotic dynamics through quasi-periodic oscillations. We apply basic tools of non-linear dynamics such as Poincaré section and maximum Lyapunov exponent to confirm the chaotic behavior of the system., (© 2019 Elsevier Inc. All rights reserved.)

Efficient farm management can be aided by the identification of zones in the landscape. These zones can be informed from different measured variables by ensuring a sense of spatial coherence. Forming spatially coherent zones is an established method in the literature, but has been found to perform poorly when data are sparse. In this paper, we describe the different types of data sparsity and investigate how this impacts the performance of established methods. We introduce a set of methodological advances that address these shortcomings to provide a method for forming spatially coherent zones under data sparsity.

This paper proposes a family of random variables for uncertainty modeling. The variables of interest have a bounded support set, and prescribed values for the first four moments. We present the feasibility conditions for the existence of any of such variables, and propose a class of variables that conforms to such constraints. This class is called staircase because the density of its members is a piecewise constant function. Convex optimization is used to calculate their distributions according to several optimality criteria, including maximal entropy and maximal log-likelihood. The flexibility and efficiency of staircases enable modeling phenomena having a possibly skewed and/or multimodal response at a low computational cost. Furthermore, we provide a means to account for the uncertainty in the distribution caused by estimating staircases from data. These ideas are illustrated by generating empirical staircase predictor models. We consider the case in which the predictor matches the sample moments exactly (a setting applicable to large datasets), as well as the case in which the predictor accounts for the sampling error in such moments (a setting applicable to sparse datasets). A predictor model for the dynamics of an aeroelastic airfoil subject to flutter instability is used as an example. The resulting predictor not only describes the system's response accurately, but also enables carrying out a risk analysis for safe flight.

In this paper, we extend the model of Liu and Zhang (Math Comput Model 54:836-845, 2011) by incorporating three control terms and apply optimal control theory to the resulting model. Optimal control strategies are proposed to minimize both the disease burden and the intervention cost. We prove the existence and uniqueness of optimal control paths and obtain these optimal paths analytically using Pontryagin's Maximum Principle. We analyse our results numerically to compare various strategies of proposed controls. It is observed that implementation of three controls is most effective and less expensive among all the strategies. Thus, we conclude that in order to reduce tuberculosis threat all the three controls must be taken into consideration concurrently., (© 2017 Elsevier Inc. All rights reserved.)

Necessity to find a non-chemical method of disease control is being increasingly felt due to its eco-friendly nature. In this paper the role of alternative food as a disease controller in a disease induced predator-prey system is studied. Stability criteria and the persistence conditions for the system are derived. Bifurcation analysis is done with respect to rate of infection. The main goal of this study is to show the non-trivial consequences of providing alternative food in a disease induced predator-prey system. Numerical simulation results illustrate that there exists a critical infection rate above which disease free system cannot be reached in absence of alternative food whereas supply of suitable alternative food makes the system disease free up to certain infection level. We have computed the disease free regions in various parametric planes. This study is aimed to introduce a new non-chemical method for controlling disease in a predator-prey system., (Copyright © 2012 Elsevier Inc. All rights reserved.)