NSFD scheme and dynamic consistency of a delayed diffusive humoral immunity viral infection model

Abstract

In this paper, we establish a delayed diffusive humoral immunity viral infection model with nonlinear incidence rate and capsids subject to the homogeneous Neumann boundary conditions. By constructing appropriate Lyapunov function, we show that the global threshold dynamics for the original continuous model. Meanwhile, nonstandard finite difference (NSFD) scheme for the original continuous model is also proposed by utilizing Micken’s method. Then, using the theory of M-matrix, it is shown that the discrete model is well-posedness. Additionally, the global stability for the steady states is investigated by constructing discrete Lyapunov function. These results imply that the NSFD scheme may preserve the dynamical properties of solutions for the original continuous model efficiently. Furthermore, some numerical simulations to illustrate the theoretical analysis are carried out.