带有标准发生率和信息干预的随机SIRS传染病模型的灭绝性和平稳分布

Extinction and Stationary Distribution of a Stochastic SIRS Epidemic Model with Standard Incidence and Information

本文考虑了一类具有标准发生率和信息干预的随机SIRS传染病模型.定义了一个停时,通过构造适当的Lyapunov函数证明了停时为无穷大,从而证明了该模型唯一正解的全局存在性.通过构造紧集和适当的Lyapunov函数,证明模型解的平稳分布的存在性及其遍历性.此外还证明了疾病的灭绝性.

In this paper, we consider a novel stochastic SIRS epidemic model with standard incidence incorporating information intervention. We first define a stopping time. Then the existence of a unique global positive solution is proved by constructing a suitable Lyapunov function to prove the stopping time is infinite. The stationary distribution and ergodicity of the model are showed by constructing a compact set and appropriate Lyapunov function. It is also proved that the extinction of the disease.