Study on HBV Infection Model with Two Kinds of Transmission Routes and Adaptive Immune Delays

In this paper, we propose a delayed HBV infection model with saturation incidence and adaptive immune response, considering two infection pathways. The model includes five compartments of uninfected hepatocytes, infected hepatocytes, free HBV virus, CTL immune response, and antibodies. Define five thresholds: infection basic reproductive number R₀, antibody immune reproductive number R₁, CTL immune reproductive number R₂, CTL immune competition reproductive number R₃ and antibody immune competition reproductive number R₄. Five kinds of equilibria of the model are obtained. By analyzing the characteristic equations and constructing suitable Lyapunov functionals and Lasalle invariance principles, the criteria for local and global asymptotic stability of each equilibrium are established.