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

2026-03-24

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Sustainability of Web economics

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.

Problem

• stochastic SIS epidemic model
• mean-reverting inhomogeneous geometric Brownian motion
• dynamical behaviors
• exponential extinction
• ergodic stationary distribution

Innovation

• stochastic SIS model
• mean-reverting inhomogeneous geometric Brownian motion
• exponential extinction
• ergodic stationary distribution
• extinction threshold