SPATIOTEMPORAL DYNAMICS OF A FRACTIONAL MODEL FOR HEPATITIS B VIRUS INFECTION WITH CELLULAR IMMUNITY

In this paper, we propose and investigate a fractional diffusive model for hepatitis B virus (HBV) infection with capsids and immune response presented by cytotoxic T lymphocyte (CTL) cells. 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-1. By constructing appropriate Lyapunov functionals, it is shown that the infection-free equilibrium is globally asymptotically stable when R-0 <= 1, the immune-free infection equilibrium is globally asymptotically stable when R-1 <= 1 < R-0 and the infection equilibrium with CTL immune response is globally asymptotically stable when R-1 > 1. Numerical simulations are performed to illustrate the analytical results.