Global attractivity of the equilibria of the diffusive SIR and SEIR epidemic models with multiple parallel infectious stages and nonlinear incidence mechanism

Abstract

In this paper, we are concerned with the diffusive SIR and SEIR epidemic models with multiple parallel infectious stages and nonlinear incidence mechanism. We first establish a priori L∞-norm estimates for the solutions to the epidemic models, and then derive the global attractivity of disease-free equilibrium and endemic equilibrium for the two models in terms of the basic reproduction number. Our results show that the diversity of infectious stages, the infection mechanism and the diffusion do not affect the global dynamics of the infectious disease.