Nonstandard finite difference scheme for a diffusive within-host virus dynamics model with both virus-to-cell and cell-to-cell transmissions

Abstract

In this paper, we first propose a diffusive within-host virus dynamics model with both virus-to-cell and cell-to-cell transmissions. Then, we consider the discretization of the model by using nonstandard finite difference scheme. It is then followed by the investigation of the global stability of the equilibria of the discrete model. Our study shows that if the basic reproduction number R0≤1, then the infection-free equilibrium is globally asymptotically stable; however if R0>1, then the infection equilibrium is globally asymptotically stable. Numerical simulations are presented to illustrate our theoretical results.