Dynamics of a Delayed Diffusive HBV Infection Model with Capsids and CTL Immune Response

Abstract

In this article, a delayed reaction-diffusion model of hepatitis B virus (HBV) infection with HBV DNA-containing capsids and cytotoxic T lymphocyte (CTL) immune response is presented and investigated by incorporating the spatial mobility of both capsids and virions. Also, the discrete time delays in the production of productively infected hepatocytes and matured capsids are taken into account in this model. First, the well-posedness of the concerned model is established in terms of existence, uniqueness, non-negativity and boundedness of solutions. The threshold conditions in terms of basic reproduction number $$R_{0}$$ and immune response reproduction number $$R_{CTL}$$ for global stability of the three spatially homogeneous steady states are established by constructing appropriate Lyapunov functions and by using linearization technique. We show that disease-free steady state, immune-free steady state and interior steady state with CTL immune response are globally asymptotically stable if $$R_{0}\le 1$$ , $$R_{CTL}\le 1<R_{0}$$ and $$R_{CTL}>1$$ , respectively. Finally, several numerical simulations are carried out in order to illustrate the theoretical results obtained.