Extinction and persistence of a stochastic HBV model

Abstract

We propose a stochastic model of the Hepatitis B Virus (HBV) and investigate viral extinction, persistence, and average residence time. To predict whether HBV will persist in the long term, we construct a crucial stochastic threshold. The establishment of this threshold faces some challenges due to the coexistence of predation and competition mechanisms in the model. To overcome this challenge, we integrate the interactions between infected hepatocytes and free virions into a unified equation, defining the crucial stochastic threshold. Our study shows that increased noise stabilizes the model when it approaches the infection-free equilibrium, but causes instability when the model approaches the infected equilibrium. This finding provides important theoretical basis for predicting HBV transmission and formulating intervention strategies. In addition, we provide detailed numerical simulations to support our conclusions.