Dynamic Analysis of an HBV Infection Model With Capsid, Distributed Delay, and Saturation CTL Immune Response

ABSTRACT This study constructs and analyzes an innovative five‐dimensional HBV infection model. This model integrates four key biological features for the first time: The role of HBV capsid, two infection routes, namely viruses‐cells (VC) and cells‐cells (CC) transmission, distributed delay to characterize the time‐lag effect in intracellular processes, and cytotoxic T lymphocyte (CTL) immune response with saturated proliferation rate. Two key threshold parameters are established: The basic reproduction number and the basic reproduction number of CTL immunity . The model has three equilibria: The infection‐free equilibrium , the immune‐free equilibrium , and the immune‐present equilibrium . By using the linearization method, Lyapunov function, and LaSalle's invariance principle, the local and global asymptotic stability of each equilibrium is rigorously proven. Our numerical simulation verifies the stability conclusion of the equilibrium. In addition, we not only consider the influence of time delay on the long‐term infection of the model, but also consider the influence of the saturation coefficient on HBV. Studies have shown that prolonging the time delay and reducing the saturation coefficient can effectively inhibit viral replication and control the spread of infection. This finding points to a new direction for public health authorities in developing novel drugs: Interventions aimed at prolonging the time delay or reducing saturation are expected to achieve effective disease control.