Asymptotical stability of a stochastic SIQRS epidemic model with log-normal Ornstein–Uhlenbeck process

Abstract

In this work, we propose and analyze a stochastic SIQRS epidemic model with the disease transmission rate driven by a log-normal Ornstein–Uhlenbeck process. By establishing a series of Lyapunov functions, we derive sufficient criteria for the asymptotical stability of the positive equilibrium of the system which suggests the prevalence of the disease in the long term. This work provides a basis for taking measures to control the disease dynamics.