The extinction and persistence of the stochastic hepatitis B epidemic model

We discuss the dynamic of a stochastic hepatitis B epidemic model. A stochastic hepatitis B model is formulated with a varying population environment for a long term behavior. The proposed model consists of three classes, namely the susceptible individuals in which the transmission rate is distributed by white noise, the infected individuals in which the same perturbation occurs and the recovered individuals. We derive sufficient conditions for the extinction and the persistence. Finally, we carry out the numerical simulations to support our analytical results.