This paper deals with a two-group stochastic SIRS epidemic model with standard incidence rates. On one hand, we establish sufficient conditions for the existence of a stationary distribution of the positive solutions to the model by constructing a suitable stochastic Lyapunov function. On the other hand, we show the sufficient conditions for the diseases to be extinct.

中文翻译：

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具有标准发病率的两组随机SIRS流行病模型的动力学行为

本文研究具有标准发病率的两组随机SIRS流行病模型。一方面，通过构造合适的随机Lyapunov函数，我们为模型的正解的平稳分布的存在建立了充分的条件。另一方面，我们显示了疾病灭绝的充分条件。