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arXiv · 2603.23675

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

Lahcen Khammich·Driss Kiouach
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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.

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Lahcen Khammich, Driss Kiouach. 2026-03-24. Dynamical behaviors of a stochastic SIS epidemic model with mean-reverting inhomogeneous geometric brownian motion. https://arxiv.org/abs/2603.23675

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