Dynamics analysis of a stochastic SIRS epidemic model with nonlinear incidence rate and transfer from infectious to susceptible

Yanmei Wang; Guirong Liu; Yanmei Wang; Guirong Liu

doi:10.3934/mbe.2019303

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 6047-6070. doi: 10.3934/mbe.2019303

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Dynamics analysis of a stochastic SIRS epidemic model with nonlinear incidence rate and transfer from infectious to susceptible

Yanmei Wang ^1,2,
Guirong Liu ^{1
,
,}

1.
School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China
2.
School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan, Shanxi 030006, China

Received: 25 February 2019 Accepted: 23 June 2019 Published: 29 June 2019

In this paper, we investigate the dynamics of a stochastic SIRS epidemic model with non-linear incidence rate and transfer from infectious to susceptible. Firstly, the existence and uniqueness of global positive solution of the model with any positive initial value are proved. Next, sufficient conditions for extinction and persistence of the disease are established. It is found that a large noise intensity has the effect of suppressing the epidemic. At last, some numerical simulations are introduced to demonstrate the theoretical results. Our results generalize and improve the existing results.
- stochastic SIRS epidemic model,
- extinction,
- persistence,
- nonlinear incidence rate
Citation: Yanmei Wang, Guirong Liu. Dynamics analysis of a stochastic SIRS epidemic model with nonlinear incidence rate and transfer from infectious to susceptible[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 6047-6070. doi: 10.3934/mbe.2019303

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Abstract

In this paper, we investigate the dynamics of a stochastic SIRS epidemic model with non-linear incidence rate and transfer from infectious to susceptible. Firstly, the existence and uniqueness of global positive solution of the model with any positive initial value are proved. Next, sufficient conditions for extinction and persistence of the disease are established. It is found that a large noise intensity has the effect of suppressing the epidemic. At last, some numerical simulations are introduced to demonstrate the theoretical results. Our results generalize and improve the existing results.

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