Dynamics for a stochastic delayed SIRS epidemic model
Articles
Xiangyun Shi
Xinyang Normal University
https://orcid.org/0000-0003-0461-0538
Yimeng Cao
Xinyang Normal University
Xueyong Zhou
Xinyang Normal University
https://orcid.org/0000-0002-7485-053X
Published 2020-09-01
https://doi.org/10.15388/namc.2020.25.17804
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Keywords

stochastic SIRS epidemic model
extinction and persistence
periodic solution
time delay

How to Cite

Shi X., Cao Y. and Zhou X. (2020) “Dynamics for a stochastic delayed SIRS epidemic model”, Nonlinear Analysis: Modelling and Control, 25(5), pp. 705–725. doi: 10.15388/namc.2020.25.17804.

Abstract

In this paper, we consider a stochastic delayed SIRS epidemic model with seasonal variation. Firstly, we prove that the system is mathematically and biologically well-posed by showing the global existence, positivity and stochastically ultimate boundneness of the solution. Secondly, some sufficient conditions on the permanence and extinction of the positive solutions with probability one are presented. Thirdly, we show that the solution of the system is asymptotical around of the disease-free periodic solution and the intensity of the oscillation depends of the intensity of the noise. Lastly, the existence of stochastic nontrivial periodic solution for the system is obtained.

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