Dynamic properties for a stochastic SEIR model with Ornstein–Uhlenbeck process

Abstract

In this article, we are committed to the study of dynamic properties for a stochastic SEIR epidemic model with infectivity in latency and home quarantine about the susceptible and Ornstein–Uhlenbeck process. Firstly, we provide a criterion for the presence of an ergodic stationary distribution of the model. Secondly, by extracting the corresponding Fokker–Planck equation, we derive the probability density function around quasi-endemic equilibrium of the stochastic model. Thirdly, we establish adequate criteria for extinction. Finally, by using the epidemic data of corresponding deterministic model, two numerical tests are presented to illustrate the effectiveness of the theoretical results.