Discretization and dynamic consistency of a delayed and diffusive viral infection model

A diffusive and delayed viral infection model with nonlinear incidence has been studied, and the global dynamical behaviors of the original model is investigated by constructing Lyapunov functionals. Furthermore, the analysis is carried out for the discrete model which is obtained by applying the nonstandard finite difference (NSFD) scheme to the original continuous model. The global stability for the corresponding equilibria is investigated by constructing discrete Lyapunov functionals as well as the positivity and boundedness of solutions of the corresponding continuous model. The results imply that the discretization scheme can efficiently preserves the qualitative properties of solutions for the original continuous model. Numerical experiments are carried out to support the theoretical results.