Qualitative investigation of cytolytic and noncytolytic immune response in an HBV model

Abstract

We investigate a mathematical model of infection by the hepatitis B virus (HBV) that includes cytolytic and noncytolytic immune response. The model exhibits a variety of steady-state solutions depending on parameter values, including nonunique and unique equilibrium solutions and periodic behavior. The disease-free equilibrium $E_f$ and the positive-disease equilibrium $E_d$ are examined. The basic reproduction ratio $R_0$ is computed in order to examine the uniqueness and local asymptotic stability of equilibria and to understand the model’s biological implications for HBV dynamics.