Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 45, pp. 1-16.

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

Authors: Bounsanong Sounvoravong (Hunan Univ., Changsha, Hunan, China)
         Shangjiang Guo (Hunan Univ., Changsha, Hunan, China)
         Yuzhen Bai (Qufu Normal Univ., Qufu China)
 
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.

Submitted June 11, 2018. Published March 30, 2019.
Math Subject Classifications: 35J20, 35J60.
Key Words: Diffusion; SIR model; basic reproduction number; stability.