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.

中文翻译：

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制度转换下具有标准发病率的随机 SIRS 流行病模型的动力学

本文的目的是介绍并启动对标准发病率的随机 SIRS 流行病模型的研究，该模型同时受到白噪声和电报噪声的干扰。我们首先显示平均值的持续性，然后建立疾病灭绝的充分条件。此外，在持久性的情况下，我们通过构造具有状态切换的合适的随机 Lyapunov 函数来获得解存在正递归的充分条件。同时，还获得了随机系统均值持续与消亡之间的阈值。最后，我们通过模拟来检验我们的理论结论。