In this paper, a stochastic epidemic system with both switching noise and white noise is proposed to research the dynamics of the diseases. Nonlinear incidence and vaccination strategies are also considered in the proposed model. By using the method of stochastic analysis, we point out the key parameters that determine the persistence and extinction of the diseases. Specifically, if [Formula: see text] is greater than 0, the stochastic system has a unique ergodic stationary distribution; while if [Formula: see text] is less than 0, the diseases will be extinct at an exponential rate.

中文翻译：

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具有非线性发病率和疫苗接种的随机切换 SIRS 流行病模型：平稳分布和消退

在本文中，提出了一种同时具有开关噪声和白噪声的随机流行病系统来研究疾病的动态。在所提出的模型中还考虑了非线性发病率和疫苗接种策略。通过随机分析的方法，我们指出了决定疾病持续和消退的关键参数。具体来说，如果[公式：见正文]大于0，则随机系统具有唯一的遍历平稳分布；而如果[公式：见正文]小于0，疾病将以指数速度灭绝。