Stationary distribution and extinction of a stochastic generalized SEI epidemic model with Ornstein-Uhlenbeck process (Q6112056)

In this paper, the authors study a stochastic SEI-type epidemic model with general transmission rates satisfying the log-normal Ornstein-Uhlenbeck process. The existence of a unique positive global solution is shown. The authors determine various threshold parameters and constructing appropriate Lyapunov functions, the prove sufficient conditions for the existence of stationary distribution and for disease extinction.