The main purpose of this paper is to study the Dynamical behaviors of a stochastic SIS epidemic model using mean-reverting inhomogeneous geometric brownian motion process. First we demonstrate the existence of a global-in-time solution and establish that is unique and remains positive. Then we derive a sufficient condition for exponential extinction of infectious diseases and we show that our extinction threshold in the stochastic case coincides with that of the deterministic case. Finaly, we define an appropriate theoretical framework to guarantee the existence of an ergodic stationary distribution.

翻译：本文旨在研究采用均值回复非齐次几何布朗运动过程的随机SIS传染病模型的动力学行为。首先，我们证明了全局时间解的存在性，并确立了其唯一性与正性保持性质。随后，我们推导了传染病指数灭绝的充分条件，并表明在随机情形下的灭绝阈值与确定性情形下的阈值一致。最后，我们定义了一个合适的理论框架，以保证遍历平稳分布的存在性。