A delayed diffusive HBV model with nonlinear incidence and CTL immune response

Abstract

In this paper, we develop a diffusive and delayed hepatitis B virus (HBV) infection model, which incorporates both virus‐to‐cell and cell‐to‐cell transmissions along with cytotoxic T lymphocyte (CTL) immune response. Two threshold parameters (basic reproduction number) and (immune response reproduction number) are defined, which determine the dynamic behavior of the model. Employing the approach of Lyapunov functionals, we show that the infection‐free steady state is globally asymptotically stable when ; the immune‐free infected steady state is globally asymptotically stable when ; and the immune‐present steady state is globally asymptotically stable when , and . We perform the sensitivity and uncertainly analysis on with respect to parameters and find that the most important parameter that drives the HBV infection is the mortality of HBV DNA capsids. Moreover, the theoretical results are supported with numerical simulations.