Abstract
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.
•A stochastic SIS epidemic model with imperfect vaccination is investigated.•When RvS>1, we establish sufficient conditions for persistence in the mean of the system.•Three conditions for the disease to die out are given, which improve the previous results on extinction of the disease.•Large noise will exponentially suppress the disease from persisting regardless of the value of RvS.