Consistent discrete global dynamics of a general initial boundary value problem for hepatitis B virus infection with capsids and adaptive immunity

Abstract

In this paper, we employ the nonstandard finite difference method to discretize a nonlinear initial boundary value problem that describes the global dynamics of hepatitis B virus infection with adaptive immunity. The model considered incorporates intracellular HBV DNA-containing capsids, a general incidence function and two categories of infected hepatocytes: exposed infected hepatocytes and productively infected hepatocytes. Adaptive immunity cells are recruited to attack all infected hepatocytes and free virus particles. The dynamics of fundamental properties of both discrete and continuous models are thoroughly studied, and it is shown that the discrete system is dynamically consistent with the continuous model. These properties include existence, nonnegativity and boundedness of solutions as well as the global stability of spatially homogeneous equilibria. We carry out some numerical simulations to support the theoretical findings and illustrate the behaviour of the solution in space and time.