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.

Global dynamical behavior of a multigroup SVIR epidemic model with Markovian switching

2021 ◽  
pp. 2150080
Author(s):  
Qun Liu ◽  
Daqing Jiang
Keyword(s):  
Markov Process ◽  
Lyapunov Function ◽  
Stochastic System ◽  
Epidemic Model ◽  
Regime Switching ◽  
Dynamical Behavior ◽  
Piecewise Deterministic Markov Process ◽  
Positive Recurrence ◽  
Persistence In The Mean ◽  
The Mean

In this paper, we are concerned with the global dynamical behavior of a multigroup SVIR epidemic model, which is formulated as a piecewise-deterministic Markov process. We first obtain sufficient criteria for extinction of the diseases. Then we establish sufficient criteria for persistence in the mean of the diseases. Moreover, in the case of persistence, we find a domain which is positive recurrence for the solution of the stochastic system by constructing an appropriate Lyapunov function with regime switching.

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.

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 Stationary Distribution and Extinction in a Stochastic SIQR Epidemic Model Incorporating Media Coverage and Markovian Switching

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1122
Author(s):  
Yanlin Ding ◽  
Jianjun Jiao ◽  
Qianhong Zhang ◽  
Yongxin Zhang ◽  
Xinzhi Ren
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Stationary Distribution ◽  
Dynamic Characteristics ◽  
Epidemic Model ◽  
Regime Switching ◽  
Media Coverage ◽  
Sufficient Conditions ◽  
Unique Positive Solution ◽  
Theoretical Results

This paper is concerned with the dynamic characteristics of the SIQR model with media coverage and regime switching. Firstly, the existence of the unique positive solution of the proposed system is investigated. Secondly, by constructing a suitable random Lyapunov function, some sufficient conditions for the existence of a stationary distribution is obtained. Meanwhile, the conditions for extinction is also given. Finally, some numerical simulation examples are carried out to demonstrate the effectiveness of theoretical results.

scholarly journals Dynamical Behavior of a Stochastic SIRC Model for Influenza A

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 745 ◽  
Author(s):  
Tongqian Zhang ◽  
Tingting Ding ◽  
Ning Gao ◽  
Yi Song
Keyword(s):  
Lyapunov Function ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Influenza A ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Global Positive Solution ◽  
Theoretical Results ◽  
Stochastic Lyapunov Function

In this paper, a stochastic SIRC epidemic model for Influenza A is proposed and investigated. First, we prove that the system exists a unique global positive solution. Second, the extinction of the disease is explored and the sufficient conditions for extinction of the disease are derived. And then the existence of a unique ergodic stationary distribution of the positive solutions for the system is discussed by constructing stochastic Lyapunov function. Furthermore, numerical simulations are employed to illustrate the theoretical results. Finally, we give some further discussions about the system.

Study on a susceptible–infected–vaccinated model with delay and proportional vaccination

2018 ◽  
Vol 11 (08) ◽  
pp. 1850102 ◽  
Author(s):  
Shuqi Gan ◽  
Fengying Wei
Keyword(s):  
Positive Solution ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Stochastic Epidemic ◽  
Persistence In The Mean ◽  
Global Positive Solution ◽  
The Mean ◽  
Stochastic Epidemic Model

A susceptible–infected–vaccinated epidemic model with proportional vaccination and generalized nonlinear rate is formulated and investigated in the paper. We show that the stochastic epidemic model admits a unique and global positive solution with probability one when constructing a proper [Formula: see text]-function therewith. Then a sufficient condition that guarantees the disappearances of diseases is derived when the indicator [Formula: see text]. Further, if [Formula: see text], then we obtain that the solution is weakly permanent with probability one. We also derived the sufficient conditions of the persistence in the mean for the susceptible and infected when another indicator [Formula: see text].

Dynamical behaviors of a prey-predator model with foraging arena scheme in polluted environments

2021 ◽  
Vol 71 (1) ◽  
pp. 235-250
Author(s):  
Xin He ◽  
Xin Zhao ◽  
Tao Feng ◽  
Zhipeng Qiu
Keyword(s):  
Periodic Solution ◽  
Stochastic System ◽  
Sufficient Conditions ◽  
Numerical Examples ◽  
Dynamical Behaviors ◽  
Analytical Results ◽  
Persistence In The Mean ◽  
The Mean ◽  
Predator Model

Abstract In this paper, a stochastic prey-predator model is investigated and analyzed, which possesses foraging arena scheme in polluted environments. Sufficient conditions are established for the extinction and persistence in the mean. These conditions provide a threshold that determines the persistence in the mean and extinction of species. Furthermore, it is also shown that the stochastic system has a periodic solution under appropriate conditions. Finally, several numerical examples are carried on to demonstrate the analytical results.

scholarly journals Stationary Distribution and Extinction of a Stochastic Microbial Flocculation Model with Regime Switching

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Haisu Zhang ◽  
Yi Song
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Theoretical Analysis ◽  
Stationary Distribution ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
Microbial Flocculation ◽  
Stochastic Lyapunov Function

In this paper, a stochastic microbial flocculation model with regime switching is developed and analyzed. By proposing a suitable stochastic Lyapunov function, the existence and ergodicity of a stationary distribution for the system are proved. Then, the extinction of microorganisms is discussed under appropriate conditions and sufficient conditions for extinction are obtained. Finally, the results of the theoretical analysis are illustrated by numerical simulation.

scholarly journals Dynamics of a stochastic phytoplankton-toxic phytoplankton-zooplankton system under regime switching

2021 ◽  
Author(s):  
He Liu ◽  
Chuanjun Dai ◽  
Hengguo Yu ◽  
Qing Guo ◽  
Jianbing Li ◽  
...  
Keyword(s):  
White Noise ◽  
Regime Switching ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Aquatic Environments ◽  
Combined Effects ◽  
Toxic Phytoplankton ◽  
Persistence In The Mean ◽  
Global Positive Solution ◽  
The Mean

In this paper, a stochastic phytoplankton-toxic phytoplankton-zooplankton system with Beddington-DeAngelis functional response, where both the white noise and regime switching are taken into account, is studied analytically and numerically. The aim of this research is to study the combined effects of the white noise, regime switching and toxin-producing phytoplankton (TPP) on the dynamics of the system. Firstly, the existence and uniqueness of global positive solution of the system is investigated. Then some sufficient conditions for the extinction, persistence in the mean and the existence of a unique ergidoc stationary distribution of the system are derived. Significantly, some numerical simulations are carried to verify our analytical results, and show that high intensity of white noise is harmful to the survival of plankton populations, but regime switching can balance the different survival states of plankton populations and decrease the risk of extinction. Additionally, it is found that an increase in the toxin liberation rate produced by TPP will increase the survival change of phytoplankton, while it will reduce the biomass of zooplankton. All these results may provide some insightful understanding on the dynamics of phytoplankton-zooplankton system in randomly disturbed aquatic environments.

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