Stationary distribution and extinction of a stochastic generalized SEI epidemic model with Ornstein–Uhlenbeck process

Abstract

In this paper, we propose a stochastic SEI epidemic model in which the transmission rates are general functions and satisfy the log-normal Ornstein–Uhlenbeck (OU) process. We first theoretically prove that there is a unique positive global solution of this stochastic model. By constructing several suitable Lyapunov functions, the sufficient condition $R_0^s>1$ is established for the existence of stationary distribution. The extinction of disease is also investigated and we find that the disease will die out at an exponential rate when $R_0^E<1$.