A non-standard finite difference scheme for a delayed and diffusive viral infection model with general nonlinear incidence rate

Abstract

A non-standard finite difference scheme is proposed to solve a delayed and diffusive viral infection model with general nonlinear incidence rate. The results show that the discrete model preserves the positivity and boundedness of solutions in order to ensure the well-posedness of the problem. Moreover, this method preserves all equilibria of the original continuous model. By constructing Lyapunov functionals, we show that the global stability of equilibria is completely determined by the basic reproduction number ℜ0, which implies that the proposed discrete model can efficiently blue preserve the global stability of equilibria of the corresponding continuous model. Numerical experiments are carried out to support the theoretical results.