Global numerical analysis of an improved IMEX numerical scheme for a reaction diffusion SIS model in advective heterogeneous environments

• Published in: Computers & mathematics with applications (1987) Vol. 144; pp. 264 - 273
• Main Authors: Liu, X., Yang, Z.W., Zeng, Y.M.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.08.2023
• Subjects: Advective environment; Globally numerical asymptotically stability; Long time behaviors; Numerical solutions; Reaction-diffusion SIS epidemic model; Reaction-diffusion SIS epidemic model; Long time behaviors; Globally numerical asymptotically stability; Numerical solutions; Advective environment
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2023.06.018

This paper presents globally numerical properties of a new numerical scheme for a reaction-diffusion advection susceptible-infected-susceptible (SIS) model. A new numerical treatment technique is introduced in spatial discretization of advection-diffusion equation, which enables the numerical solutions to preserve the stability and positivity with less stepsize restrictions. The convergence, biological significance and globally stability of numerical solutions is explored in the paper. A threshold value, named by numerical basic reproduction number and denoted by R0Δx, is introduced in the numerical stability analysis of the model. It is proved the numerical disease free equilibrium (DFE) is globally asymptotically stable if R0Δx<1 and unstable if R0Δx>1. It is shown the numerical basic number R0Δx replicates the asymptotic behaviors of the basic reproduction number R0 for the model. Some numerical experiments are given in the end to confirm the conclusions.