Long time numerical properties analysis of a diffusive SIS epidemic model under a linear external source

Abstract

This paper deals with the numerical properties of a reaction-diffusion susceptible infected susceptible (SIS) epidemic model under a linear external source. A numerical scheme is constructed with a finite difference scheme for the space discretization and an Implicit-Explicit (IMEX) method in time integration. A threshold value, numerical basic reproduction number, is proposed in the long-time stability analysis of numerical solutions. Differently from previous works on the same model, the numerical basic reproduction number can preserve the behaviors of the basic reproduction number of the model, towards which it converges when the spatial stepsize vanishes. Moreover, it plays a role for the discrete dynamics similar to the one played by its continuous counterpart. Some numerical experiments are given in the end to confirm the conclusions and detect the conjecture on the stability of endemic equilibrium (EE) in general case.