Abstract
In this paper, we consider a stochastic non-autonomous SISV epidemic model. For the non-autonomous periodic system, firstly, we get the threshold of the system which determines whether the epidemic occurs or not. Then in the case of persistence, we show that there exists at least one nontrivial positive periodic solution of the stochastic system.
•A stochastic non-autonomous SISV epidemic model is proposed and studied.•We get the threshold of the system which determines whether the epidemic occurs or not.•There exists at least one nontrivial positive periodic solution of the stochastic system.