Dynamic Of Stochastic SISV Epidemic Model In A Population With Varying Size

In this paper, we extend some deterministic epidemics model by inducing a white .oise in the model, and get a stochastic SISV epidemics model with where B(t) is a standard Brownian Motion, σ2 is the white noise intensity.Firstly, we prove the global existence and uniqueness of positive solution of SISV by variable transformation and the theory of existence and uniqueness of solution for stochas-tic differential equation; Secondly, we conclude that the disappearance and epidemic of the infectious diseases through the study of extinction and persistence; Finally, we anal-yse and study the asymptotic behavior of the solution of the model in the corresponding deterministic model around the endemic proportion equilibrium.