scholarly journals Dynamics of a Stochastic SIRS Epidemic Model with Regime Switching and Specific Functional Response

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Amine EL Koufi ◽  
Abdelkrim Bennar ◽  
Noura Yousfi
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Regime Switching ◽  
Unique Positive Solution ◽  
Sirs Epidemic Model ◽  
Sirs Model ◽  
Incident Rate ◽  
Stochastic Sirs Epidemic Model

The purpose of this work is to investigate the dynamic behaviors of the SIRS epidemic model with nonlinear incident rate under regime switching. We establish the existence of a unique positive solution of our system. Furthermore, we obtain the conditions for the extinction of diseases, and we show the existence of the stationary distribution for our stochastic SIRS model under regime switching. Numerical simulations are employed to illustrate our theoretical analysis.

scholarly journals Ergodicity of a Nonlinear Stochastic SIRS Epidemic Model with Regime-Switching Diffusions

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Hongxia Liu ◽  
Juan Li ◽  
Mengnan Chi ◽  
Jinlei Liu ◽  
Wencai Zhao
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
Threshold Parameter ◽  
Sirs Epidemic Model ◽  
Switching Diffusions ◽  
White Noises ◽  
Stochastic Sirs Epidemic Model

In this paper, taking both white noises and colored noises into consideration, a nonlinear stochastic SIRS epidemic model with regime switching is explored. The threshold parameter R s is found, and we investigate sufficient conditions for the existence of the ergodic stationary distribution of the positive solution. Finally, some numerical simulations are also carried out to demonstrate the analytical results.

Dynamic Analysis of an SIRS Model with Nonlinear Incidence Rate

2012 ◽  
Vol 155-156 ◽  
pp. 23-26
Author(s):  
Jun Hong Li ◽  
Ning Cui ◽  
Liang Cui ◽  
Cai Juan Li
Keyword(s):  
Hopf Bifurcation ◽  
Dynamic Analysis ◽  
Numerical Simulations ◽  
Epidemic Model ◽  
Global Dynamics ◽  
Nonlinear Incidence Rate ◽  
Dulac Function ◽  
Sirs Epidemic Model ◽  
Sirs Model ◽  
Disease Free

In this paper, we study the global dynamics of an SIRS epidemic model with nonlinear inci- dence rate. By means of Dulac function and Poincare-Bendixson Theorem, we proved the global asy- mptotical stable results of the disease-free equilibrium. It is then obtained the model undergoes Hopf bifurcation and existence of one limit cycle. Some numerical simulations are given to illustrate the an- alytical results.

Dynamics of a stochastic SIRS epidemic model with standard incidence under regime switching

2021 ◽  
pp. 2150074
Author(s):  
Jiang Xu ◽  
Yinong Wang ◽  
Zhongwei Cao
Keyword(s):  
Lyapunov Function ◽  
Stochastic System ◽  
Epidemic Model ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
Sirs Epidemic Model ◽  
Persistence In The Mean ◽  
The Mean ◽  
Stochastic Sirs Epidemic Model ◽  
Stochastic Lyapunov Function

The goal of this paper is to introduce and initiate a study of a stochastic SIRS epidemic model with standard incidence which is perturbed by both white and telegraph noises. We first show persistence in the mean and then establish the sufficient conditions for extinction of the disease. Moreover, in the case of persistence, we obtain sufficient conditions for the existence of positive recurrence of the solutions by means of structuring suitable stochastic Lyapunov function with regime switching. Meanwhile, the threshold between persistence in the mean and extinction of the stochastic system is also obtained. Finally, we test our theory conclusion by simulations.

scholarly journals The Positivity of Numerical Method for Susceptible-Infected-Recovered-Susceptible Epidemic Model

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Feng Feng ◽  
Zong Wang
Keyword(s):  
Analytical Solution ◽  
Numerical Solution ◽  
Numerical Method ◽  
Epidemic Model ◽  
Numerical Technique ◽  
Environmental Perturbations ◽  
Sirs Epidemic Model ◽  
Sirs Model ◽  
Balanced Implicit Method ◽  
Stochastic Sirs Epidemic Model

Sudden environmental perturbations may affect the positivity of the solution of the susceptible-infected-recovered-susceptible (SIRS) model. Most of the SIRS epidemic models have no analytical solution. Thus, in order to find the appropriate solution, the numerical technique becomes more essential for us to solve the dynamic behavior of epidemics. In this paper, we are concerned with the positivity of the numerical solution of a stochastic SIRS epidemic model. A new numerical method that is the balanced implicit method (BIM) is set, which preserves the positivity under given conditions. The BIM method can maintain positive numerical solution. An illustrative numerical instance is presented for the numerical BIM of the stochastic SIRS model.

Dynamics of a stochastic periodic SIRS model with time delay

2020 ◽  
pp. 2050072
Author(s):  
Xiangyun Shi ◽  
Yimeng Cao
Keyword(s):  
Time Delay ◽  
Numerical Simulations ◽  
Epidemic Model ◽  
Lyapunov Functions ◽  
Ultimate Boundedness ◽  
Sirs Epidemic Model ◽  
Dynamical Behaviors ◽  
Sirs Model ◽  
Global Positive Solution ◽  
Stochastically Ultimate Boundedness

Dynamical behaviors of a stochastic periodic SIRS epidemic model with time delay are investigated. By constructing suitable Lyapunov functions and applying Itô’s formula, the existence of the global positive solution and the property of stochastically ultimate boundedness of model (1.1) are proved. Moreover, the extinction and the persistence of the disease are established. The results are verified by numerical simulations.

scholarly journals Threshold dynamics for a class of stochastic SIRS epidemic models with nonlinear incidence and Markovian switching

2021 ◽  
Author(s):  
Amine EL Koufi ◽  
Abdelkrim Bennar ◽  
Noura Yousfi ◽  
M Pitchaimani
Keyword(s):  
Numerical Simulations ◽  
Stochastic System ◽  
Epidemic Model ◽  
Stochastic Calculus ◽  
Markovian Switching ◽  
Threshold Dynamics ◽  
Nonlinear Incidence ◽  
Sirs Epidemic Model ◽  
Stochastic Sirs Epidemic Model ◽  
Theoretical Results

In this paper, we consider a stochastic SIRS epidemic model with nonlinear incidence and Markovian switching. By using the stochastic calculus background, we establish that the stochastic threshold R_{ swt}  can be used to determine the compartment dynamics of the stochastic system. Some examples and numerical simulations are presented to confirm the theoretical results established in this paper.

Dynamics of a stochastic susceptible-infective-recovered (SIRS) epidemic model with vaccination and nonlinear incidence under regime switching and Lévy jumps

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Junna Hu ◽  
Buyu Wen ◽  
Ting Zeng ◽  
Zhidong Teng
Keyword(s):  
Epidemic Model ◽  
Regime Switching ◽  
Markov Switching ◽  
Threshold Value ◽  
Open Problems ◽  
Nonlinear Incidence ◽  
Sirs Epidemic Model ◽  
Stochastic Epidemic ◽  
Lévy Jumps ◽  
White Noises

Abstract In this paper, a stochastic susceptible-infective-recovered (SIRS) epidemic model with vaccination, nonlinear incidence and white noises under regime switching and Lévy jumps is investigated. A new threshold value is determined. Some basic assumptions with regard to nonlinear incidence, white noises, Markov switching and Lévy jumps are introduced. The threshold conditions to guarantee the extinction and permanence in the mean of the disease with probability one and the existence of unique ergodic stationary distribution for the model are established. Some new techniques to deal with the Markov switching, Lévy jumps, nonlinear incidence and vaccination for the stochastic epidemic models are proposed. Lastly, the numerical simulations not only illustrate the main results given in this paper, but also suggest some interesting open problems.

scholarly journals Comparison of deterministic and stochastic SIRS epidemic model with saturating incidence and immigration

2014 ◽  
Vol 4 (2) ◽  
pp. 101-116 ◽  
Author(s):  
Aadil Lahrouz ◽  
Lahcen Omari ◽  
Adel Settati ◽  
Aziza Belmaâti
Keyword(s):  
Epidemic Model ◽  
Sirs Epidemic Model ◽  
Stochastic Sirs Epidemic Model

Dynamic behavior of a stochastic SIRS model with two viruses

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jiandong Zhao ◽  
Tonghua Zhang ◽  
Zhixia Han
Keyword(s):  
Growth Rate ◽  
Asymptotic Stability ◽  
Global Existence ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Sufficient Conditions ◽  
Environmental Noise ◽  
Sirs Model ◽  
The Moment ◽  
Disease Free

AbstractTo study the effect of environmental noise on the spread of the disease, a stochastic Susceptible, Infective, Removed and Susceptible (SIRS) model with two viruses is introduced in this paper. Sufficient conditions for global existence of positive solution and stochastically asymptotic stability of disease-free equilibrium in the model are given. Then, it is shown that the positive solution is stochastically ultimately bounded and the moment average in time of the positive solution is bounded. Our results mean that the environmental noise suppresses the growth rate of the individuals and drives the disease to extinction under certain conditions. Finally, numerical simulations are given to illustrate our main results.

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