Global Properties of a HBV Infection Model with HBV DNA-Containing Capsids and CTL Immune Response

Abstract

In this paper, the global dynamical behavior of a hepatitis B virus (HBV) infection model with HBV DNA-containing capsids and cytotoxic T lymphocytes (CTLs) immune response is investigated. We derive the conditions for global asymptotic stability of the steady states of the model in terms of the basic reproduction number $$R_{0}$$ and the immune response reproduction number $$R_{{ CTL}}$$ . By constructing appropriate Lyapunov functions, it is shown that the disease-free steady state is globally asymptotically stable when $$R_{0}\le 1$$ , the immune-free steady state is globally asymptotically stable when $$R_{{ CTL}}\le 1<R_{0}$$ and the endemic steady state is globally asymptotically stable when $$R_{{ CTL}}>1$$ . Further, we incorporate two discrete delays in the model to account for the intracellular delays in the production of productively infected hepatocytes and capsids. We also derive the global properties of this two-delay model in terms of $$R_{0}$$ and $$R_{{ CTL}}$$ . Finally, illustrative numerical simulations are presented to support our theoretical findings.