A note on the stationary distribution of stochastic SEIR epidemic model with saturated incidence rate

Abstract

Abstract The stochastic SEIR infectious diseases model with saturated incidence rate is studied in this paper. By constructing appropriate Lyapunov functions, we show that there is a stationary distribution for the system and the ergodicity holds provided $${R}_{0}^{s}$$ R 0 s > 1. In particular, we improve the results obtained by previous studies greatly, condition in our Theorem is more concise and elegant.