Epidemic Model Research Articles

Asymptotic profiles of a nonlocal dispersal SIS epidemic model with saturated incidence

Asymptotic profiles of a nonlocal dispersal SIS epidemic model with saturated incidence

Dynamical behavior of a hepatitis B epidemic model and its NSFD scheme

AbstractHepatitis is inflammation of the liver, and one of its types, hepatitis B, is a contagious infection. Using mathematical models, the nature of the spread of the Hepatitis B virus can be predicted. In the present paper, a hepatitis B epidemic model with a Beddington–DeAngelis type incidence rate and a constant vaccination rate is considered. Some dynamical properties of this model, such as non-negativity, boundedness character, the basic reproduction number $$\mathcal {R}_0$$ R 0 , stability nature, and the bifurcation phenomenon, are investigated. By the Bendixson theorem, it is demonstrated that the disease-free equilibrium is globally asymptotically stable. It is shown that a transcritical bifurcation phenomenon occurs when $$\mathcal {R}_0=1$$ R 0 = 1 . It is concluded that the endemic equilibrium is globally asymptotically stable when $$\mathcal {R}_0>1$$ R 0 > 1 , by utilizing Dulac’s criteria. Also, a discrete system of difference equations is obtained by constructing a non-standard finite difference (NSFD) scheme for the continuous model. It is shown that the solutions of this discrete system are dynamically consistent for all finite step sizes. The theoretical results obtained are also supported and visualized by numerical simulations. These simulations also demonstrate that the NSFD scheme produces much more efficient results than the Euler or RK4 schemes, as shown in the theoretical results obtained.

Biased versus unbiased numerical methods for stochastic simulations

Approximate numerical methods are one of the most used strategies to extract information from many-interacting-agents systems. In particular, numerical approximations are of extended use to deal with epidemic, ecological and biological models, since unbiased methods like the Gillespie algorithm can become unpractical due to high CPU time usage required. However, the use of approximations has been debated and there is no clear consensus about whether unbiased methods or biased approach is the best option. In this work, we derive scaling relations for the errors in approximations based on binomial extractions. This finding allows us to build rules to compute the optimal values of both the discretization time and number of realizations needed to compute averages with the biased method with a target precision and minimum CPU-time usage. Furthermore, we also present another rule to discern whether the unbiased method or biased approach is more efficient. Ultimately, we will show that the choice of the method should depend on the desired precision for the estimation of averages.

Flip bifurcation analysis and mathematical modeling of cholera disease by taking control measures

To study the dynamical system, it is necessary to formulate the mathematical model to understand the dynamics of various diseases which are spread in the world wide. The objective of the research study is to assess the early diagnosis and treatment of cholera virus by implementing remedial methods with and without the use of drugs. A mathematical model is built with the hypothesis of strengthening the immune system, and a ABC operator is employed to turn the model into a fractional-order model. A newly developed system SEIBR, which is examined both qualitatively and quantitatively to determine its stable position as well as the verification of flip bifurcation has been made for developed system. The local stability of this model has been explored concerning limited observations, a fundamental aspect of epidemic models. We have derived the reproductive number using next generation method, denoted as “R0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R_{0}$$\\end{document}”, to analyze its impact rate across various sub-compartments, which serves as a critical determinant of its community-wide transmission rate. The sensitivity analysis has been verified according to its each parameters to identify that how much rate of change of parameters are sensitive. Atangana–Toufik scheme is employed to find the solution for the developed system using different fractional values which is advanced tool for reliable bounded solution. Also the error analysis has been made for developed scheme. Simulations have been made to see the real behavior and effects of cholera disease with early detection and treatment by implementing remedial methods without the use of drugs in the community. Also identify the real situation the spread of cholera disease after implementing remedial methods with and without the use of drugs. Such type of investigation will be useful to investigate the spread of virus as well as helpful in developing control strategies from our justified outcomes.

Modeling and analysis of the fractional-order epidemic model to investigate mutual influence in HIV/HCV co-infection

Modeling and analysis of the fractional-order epidemic model to investigate mutual influence in HIV/HCV co-infection

Dynamical Behavior and Numerical Simulation of an Influenza A Epidemic Model with Log-Normal Ornstein–Uhlenbeck Process

Dynamical Behavior and Numerical Simulation of an Influenza A Epidemic Model with Log-Normal Ornstein–Uhlenbeck Process

Optimal Control for an Epidemic Model of COVID-19 with Time-Varying Parameters

The coronavirus disease 2019 (COVID-19) pandemic disrupted public health and economies worldwide. In this paper, we investigate an optimal control problem to simultaneously minimize the epidemic size and control costs associated with intervention strategies based on official data. Considering people with undetected infections, we establish a control system of COVID-19 with time-varying parameters. To estimate these parameters, a parameter identification scheme is adopted and a mixed algorithm is constructed. Moreover, we present an optimal control problem with two objectives that involve the newly increased number of infected individuals and the control costs. A numerical scheme is conducted, simulating the epidemic data pertaining to Shanghai during the period of 2022, caused by the Omicron variant. Coefficient combinations of the objectives are obtained, and the optimal control measures for different infection peaks are indicated. The numerical results suggest that the identification variables obtained by using the constructed mixed algorithm to solve the parameter identification problem are feasible. Optimal control measures for different epidemic peaks can serve as references for decision-makers.

Study of the Six-Compartment Nonlinear COVID-19 Model with the Homotopy Perturbation Method

The current study aims to utilize the homotopy perturbation method (HPM) to solve nonlinear dynamical models, with a particular focus on models related to predicting and controlling pandemics, such as the SIR model. Specifically, we apply this method to solve a six-compartment model for the novel coronavirus (COVID-19), which includes susceptible, exposed, asymptomatic infected, symptomatic infected, and recovered individuals, and the concentration of COVID-19 in the environment is indicated by S(t), E(t), A(t), I(t), R(t), and B(t), respectively. We present the series solution of this model by varying the controlling parameters and representing them graphically. Additionally, we verify the accuracy of the series solution (up to the (n−1)th-degree polynomial) that satisfies both the initial conditions and the model, with all coefficients correct at 18 decimal places. Furthermore, we have compared our results with the Runge–Kutta fourth-order method. Based on our findings, we conclude that the homotopy perturbation method is a promising approach to solve nonlinear dynamical models, particularly those associated with pandemics. This method provides valuable insight into how the control of various parameters can affect the model. We suggest that future studies can expand on our work by exploring additional models and assessing the applicability of other analytical methods.

Global Stability of SIR Model with Heterogeneous Transmission Rate Modeled by the Preisach Operator

Global Stability of SIR Model with Heterogeneous Transmission Rate Modeled by the Preisach Operator

A risk-induced dispersal strategy of the infected population for a disease-free state in the SIS epidemic model

This article proposes a dispersal strategy for infected individuals in a spatial susceptible-infected-susceptible (SIS) epidemic model. The presence of spatial heterogeneity and the movement of individuals play crucial roles in determining the persistence and eradication of infectious diseases. To capture these dynamics, we introduce a moving strategy called risk-induced dispersal (RID) for infected individuals in a continuous-time patch model of the SIS epidemic. First, we establish a continuous-time n-patch model and verify that the RID strategy is an effective approach for attaining a disease-free state. This is substantiated through simulations conducted on 7-patch models and analytical results derived from 2-patch models. Second, we extend our analysis by adapting the patch model into a diffusive epidemic model. This extension allows us to explore further the impact of the RID movement strategy on disease transmission and control. We validate our results through simulations, which provide the effects of the RID dispersal strategy.

Optimal control analysis of COVID-19 stochastic model with comprehensive strategies

In this paper, we construct a stochastic SVEAIR (Susceptible-Vaccinated-Exposed -Asymptomatic-Infected-Removed) epidemic model. It aimed to investigate COVID-19 control strategies through four different control methods, which consist of prophylaxis, vaccination control, rapid screening of people in exposure categories, and people identified as infected without screening. Firstly, we study the optimal control model and obtain the optimal control strategy using stochastic control theory. Secondly, the optimal control model with control term or without control term is numerically analyzed by using the implicit Runge-Kutta approximation method. At last, The numerical simulations verify the theoretical results and it show that control could help reduce infection and improve population health.

Tight or Loose: Analysis of the Organization Cognition Process of Epidemic Risk and Policy Selection

In the context of Disease X risks, how governments and public health authorities make policy choices in response to potential epidemics has become a topic of increasing concern. The tightness of epidemic prevention policies is related to the effectiveness of the implementation of measures, while the organizational cognition of epidemic risks is related to the rationality of policy choices. During the three years of COVID-19, the Chinese government constantly adjusted the tightness of its prevention policies as awareness of the epidemic risk improved. Therefore, based on the epidemic risk organizational cognition model, the key nodes that affect the tightness of epidemic prevention policies can be explored to find the organizational behavior rules behind the selection of prevention policies. Firstly, through observing the adjustments made to the Chinese government’s prevention strategies during the epidemic, a time-series cross-case comparative analysis reveals how policy tightness shifted from stringent to lenient. This shift coincided with the organizational cognition of epidemic risk evolving from vague to clear. Secondly, by building the “knowledge-cognition” coordinate system to draw the organizational cognition spiral of epidemic risk, it is clear that the changes in the tightness of the prevention policies mainly came from the internalization and externalization of knowledge such as epidemic risk characteristics to promote the level of organizational cognition, which is manifested as expansion and deepening. Thirdly, the node changes in the interaction between organizational cognition development and policy choice proved that different stages of the epidemic had diverse environmental parameters. Moreover, as the epidemic nears its end, the focus of policy tightness is shifting from policy objectives to policy implementation around governance tools. The results indicate that organizational cognition of epidemic risk exhibits significant stages and periodicity. Additionally, epidemic risk characteristics, environmental coupling, and governance tools are crucial factors in determining the tightness of epidemic prevention policies.

Temporal logics for compartmental models

Abstract This paper introduces two logic frameworks for the study of SIR (Susceptible-Infected-Recovered) and SIRS compartmental epidemic models, one based on Linear Temporal Logic and the other on Computation Tree Logic. We provide a short literature overview on compartmental models and other related works using logics, and then define our logics with their respective axiomatizations, and demonstrate their soundness and completeness proofs.

Dynamic analysis of a SIS epidemic model with nonlinear incidence and ratio dependent pulse control

Dynamic analysis of a SIS epidemic model with nonlinear incidence and ratio dependent pulse control

Study on SEAI Model of COVID-19 Based on Asymptomatic Infection

In this paper, an SEAI epidemic model with asymptomatic infection is studied under the background of mass transmission of COVID-19. First, we use the next-generation matrix method to obtain the basic reproductive number R0 and calculate the equilibrium point. Secondly, when R0<1, the local asymptotic stability of the disease-free equilibrium is proved by Hurwitz criterion, and the global asymptotic stability of the disease-free equilibrium is proved by constructing the Lyapunov function. When R0>1, the system has a unique endemic equilibrium point and is locally asymptotically stable, and it is also proved that the system is uniformly persistent. Then, the application of optimal control theory is carried out, and the expression of the optimal control solution is obtained. Finally, in order to verify the correctness of the theory, the stability of the equilibrium point is numerically simulated and the sensitivity of the parameters of R0 is analyzed. We also simulated the comparison of the number of asymptomatic infected people and symptomatic infected people before and after adopting the optimal control strategy. This shows that the infection of asymptomatic people cannot be underestimated in the spread of COVID-19 virus, and an isolation strategy should be adopted to control the spread speed of the disease.

Dynamic properties, probability density, and estimation of an SIRIS epidemic model with an Ornstein-Uhlenbeck process

Abstract Considering the relapse and temporary immunity of some diseases, a stochastic SIRIS epidemic model with saturation incidence is developed in this paper, in which the Ornstein-Uhlenbeck process is introduced to describe the randomness of the model. The existence and uniqueness of the global solution are first proved to investigate the dynamic properties of the SIRIS model. By constructing a series of Lyapunov functions, the thresholds $\sR_0^E$ and $\sR_0^S$ are further derived to determine the extinction and persistence of the disease. Subsequently, we prove that the solution of the model admits a stationary distribution. The probability density function is obtained by the algebraic method. In addition, the unknown parameters of the density function are estimated by using the maximum likelihood estimation. Finally, numerical simulations verify the results of the above properties.

Analyses of the SIR Epidemic Model Including Treatment and Immigration

This paper aims to examine the dynamics of a variation of a nonlinear SIR epidemic model. We analyze the complex dynamic nature of the discrete-time SIR epidemic model by discretizing a continuous SIR epidemic model subject to treatment and immigration effects with the Euler method. First of all, we show the existence of equilibrium points in the model by reducing the three-dimensional system to the two-dimensional system. Next, we show the stability conditions of the obtained positive equilibrium point and the visibility of flip bifurcation. A feedback control strategy is applied to control the chaos occurring in the system after a certain period of time. We also perform numerical simulations to support analytical results. We do all these analyses for models with and without immigration and show the effect of immigration on dynamics.

The Threshold of a Stochastic SIRS Epidemic Model with a General Incidence

The Threshold of a Stochastic SIRS Epidemic Model with a General Incidence

Fractional dynamics and sensitivity analysis of measles epidemic model through vaccination

Measles is a highly contagious disease that mainly affects children worldwide. Even though a reliable and effective vaccination is available, there were 140,000 measles deaths worldwide in 2018, and most of them were children under the age five years. In this paper, we comprehensively investigate a novel fractional SVEIR (Susceptible-Vaccinated-Exposed-Infected-Recovered) model of the measles epidemic powered by nonlinear fractional differential equations to understand the epidemic’s dynamical behaviour. We use a non-singular Atangana-Baleanu fractional derivative to analyze the proposed model, taking advantage of non-locality. The existence, uniqueness, positivity and boundedness of the solutions are shown via concepts of fixed point theory, and we also perform the Ulam-Hyers stability of the considered model. The parameter sensitivity is discussed in the context of the variance with each parameter using 3-D graphics based on the basic reproduction number. Moreover, with the Atangana-Toufik numerical scheme, numerical findings are depicted for different fractional-order values. The presented approach produce results that are efficiently consistent and in excellent agreement with the theoretical results.

A new virus-centric epidemic modeling approach, 2: Simulation of deceased of SARS CoV 2 in several countries

A new virus-centric epidemic modeling approach, 2: Simulation of deceased of SARS CoV 2 in several countries