A stochastic SIHR epidemic model with general population-size dependent contact rate and Ornstein-Uhlenbeck process dynamics analysis

Abstract The purpose of this work is to investigate a novel stochastic SIHR epidemic model, which includes a general incidence rate and mean-reversion Ornstein-Uhlenbeck process. Firstly, the existence of global positivity of the solution is testified by Lyapunov function. Secondly, this disease will be eradicated if R0s < 1 . Otherwise, if R0* > 1, then the system has a stationary distribution, which means that the pandemic will persist. In addition, an explicit expression of the probability density function for a linear system near quasi-endemic equilibrium is obtained under certain conditions. Finally, a series of numerical simulations are carried out to validate the theoretical conclusions.