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arXiv · 1806.08696

On invariant measures and the asymptotic behavior of a stochastic delayed SIRS epidemic model

Xiaoming Fu
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Abstract

In this paper, we consider a stochastic epidemic model with time delay and general incidence rate. We first prove the existence and uniqueness of the global positive solution. By using the Krylov-Bogoliubov method, we obtain the existence of invariant measures. Furthermore , we study a special case where the incidence rate is bilinear with distributed time delay. When the basic reproduction number R0 < 1, the analysis of the asymptotic behavior around the disease-free equilibrium E0 is provided while when R0 > 1, we prove that the invariant measure is unique and ergodic. The numerical simulations also validate our analytical results.

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Xiaoming Fu. 2018-06-21. On invariant measures and the asymptotic behavior of a stochastic delayed SIRS epidemic model. https://doi.org/10.1016/j.physa.2019.04.181

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