Bifurcation analysis of a delayed epidemic model with diffusion
Commun. Korean Math. Soc. 2011 Vol. 26, No. 2, 321-338
Printed June 1, 2011
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
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