Stationary distribution and density function analysis of a stochastic epidemic HBV model

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 mu omega nu C 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 rho(S)(0) corresponding to the basic reproduction number of ODE system. This implies the persistence of the diseases when rho(s)(0) > 1. Meanwhile, the sufficient conditions for the extinction of the diseases are derived when rho(T)(0) < 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. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

This paper presents a stochastic HBV infection model and investigates its dynamic behaviors. It establishes the existence and ergodicity of the model's stationary distribution, determines the critical value corresponding to the basic reproduction number, and provides conditions for disease persistence or extinction. The specific expression of the probability density function around the endemic quasi-equilibrium is also derived, and numerical simulations confirm theoretical results and match HBV epidemic data in China.