Dynamical behavior of a stochastic COVID-19 model with two Ornstein–Uhlenbeck processes and saturated incidence rates

According to the transmission characteristics of COVID-19, this paper proposes a stochastic SAIRS epidemic model with two mean reversion Ornstein–Uhlenbeck processes and saturated incidence rates. We first prove the existence and uniqueness of the global solution in the stochastic model. Using several suitable Lyapunov methods, we then derive the extinction and persistence of COVID-19 under certain conditions. Further, stationary distribution and ergodic properties are obtained. Moreover, we obtain the probability density function of the stochastic model around the equilibrium. Numerical simulations illustrate our theoretical results and the effect of essential parameters. Finally, we apply the model to investigate the latest outbreak of the COVID-19 epidemic in Guangzhou city, China.