Bifurcation and stability of a diffusive SIRS epidemic model with time delay

Abstract

In this article, we study a reaction-diffusion system for a SIRS epidemic model with time delay and nonlinear incidence rate. On the one hand, we study the existence and stability of the disease-free equilibrium, endemic equilibria and Hopf bifurcation, by analyzing the characteristic equations. On the other hand, we establish formulas determining the direction and stability of the bifurcating periodic solutions.