The threshold of a stochastic SIS epidemic model with imperfect vaccination

In this paper, we analyze the threshold RvS of a stochastic SIS epidemic model with partially protective vaccination of efficacy e∈[0,1]. Firstly, we show that there exists a unique global positive solution of the stochastic system. Then RvS>1 is verified to be sufficient for persistence in the mean of the system. Furthermore, three conditions for the disease to die out are given, which improve the previously-known results on extinction of the disease. We also obtain that large noise will exponentially suppress the disease from persisting regardless of the value of the basic reproduction number RvS.