Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

HOME ALL ARTICLES View

Commun. Korean Math. Soc. 2011; 26(2): 321-338

Printed June 1, 2011

https://doi.org/10.4134/CKMS.2011.26.2.321

Copyright © The Korean Mathematical Society.

Bifurcation analysis of a delayed epidemic model with diffusion

Changjin Xu and Maoxin Liao

Guizhou College of Finance and Economics, Central South University

Abstract

In this paper, a class of delayed epidemic model with diffusion is investigated. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation are also carried out to support our analytical findings. Finally, biological explanations and main conclusions are given.

Keywords: epidemic model, diffusion, delay, stability, Hopf bifurcation

MSC numbers: 34K20, 34C25