Dynamical behaviors of a stochastic SIS epidemic model with mean-reverting inhomogeneous geometric brownian motion

TL;DR

This paper analyzes a stochastic SIS epidemic model driven by mean-reverting inhomogeneous geometric Brownian motion, establishing conditions for disease extinction and the existence of a stationary distribution.

Contribution

It introduces a stochastic SIS model with mean-reverting noise, providing new insights into its extinction criteria and long-term behavior.

Findings

Global-in-time positive solution exists and is unique.

Sufficient condition for exponential disease extinction matches the deterministic case.

An ergodic stationary distribution exists under certain conditions.

Abstract

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.