Abstract
In this paper, we present a stochastic hepatitis B virus (HBV) infection model and the dynamic behaviors of the model are investigated. When the fraction of vertical transmission μωνC is not considered to be new infections, the existence and ergodicity of the stationary distribution of the model are obtained by constructing a suitable Lyapunov function, which determines a critical value ρ0s corresponding to the basic reproduction number of ODE system. This implies the persistence of the diseases when ρ0s>1. Meanwhile, the sufficient conditions for the extinction of the diseases are derived when ρ0T<0. What is more, we give the specific expression of the probability density function of the stochastic model around the unique endemic quasi-equilibrium by solving the Fokker–Planck equation. Finally, the numerical simulations are illustrated to verify the theoretical results and match the HBV epidemic data in China.
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