Threshold behaviors and density function of a stochastic parasite-host epidemic model with Ornstein–Uhlenbeck process

Abstract

In this paper, a stochastic parasite-host epidemic model is investigated. To simulate the unavoidable effects of environmental perturbations on the model, the disease transmission rate is assumed to satisfy a log-normal Ornstein–Uhlenbeck process. We study the stationary distribution and extinction of the disease and find a critical value $R_0^s$, which serves as a threshold determining the persistence or extinction of the disease. Furthermore, the exact local expression for the density function of the stochastic model around the quasi-epidemic equilibrium is derived.