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 R0s>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 R0E<1.
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