A threshold of a delayed stochastic epidemic model with Crowly–Martin functional response and vaccination

Abstract In this paper, we study a delayed stochastic SIR epidemic model with Crowly–Martin functional response and vaccination. First we prove the existence and the uniqueness of the positive solution. Therefore, we establish a stochastic threshold R s as a sufficient condition for the extinction and persistence in mean of the stochastic epidemic system. Finally, numerical simulations are presented to support our theoretical results.