In this paper, based on our recent work (Zhang and Zhang, 2021), we introduce multiple perturbations in an SIS epidemic model with isolation and varying total population size. We present the threshold $R_s$ of the model. When $R_s$ is less than 1, we prove that the disease will die out. When $R_s$ is greater than 1, we construct an appropriate stochastic Lyapunov function and using the well-known Khasminskii’s theory, prove the existence of the stationary distribution. This has important significance to obtain the statistical characteristics of the infectious disease such as the mean, variance and so on.

中文翻译：

---

总人口规模变化的随机SIQS流行病模型的平稳分布

在本文中，基于我们最近的工作（Zhang和Zhang，2021年），我们在SIS流行病模型中引入了多个扰动，具有孤立性和总人口规模的变化。我们提出了门槛${\mathrm{[R}}_s$模型的 什么时候${\mathrm{[R}}_s$小于1，我们证明疾病会消失。什么时候${\mathrm{[R}}_s$大于1，我们构造了一个适当的随机Lyapunov函数，并使用著名的Khasminskii理论，证明了平稳分布的存在。这对于获得传染病的统计特征（如均值，方差等）具有重要意义。