Electron. J. Diff. Eqns., Vol. 2007(2007), No. 77, pp. 1-17.

Bifurcation analysis on a delayed SIS epidemic model with stage structure

Li Liu, Xiangao Li, Kejun Zhuang

Abstract:
In this paper, a delayed SIS (Susceptible Infectious Susceptible) model with stage structure is investigated. We study the Hopf bifurcations and stability of the model. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. The conditions to guarantee the global existence of periodic solutions are established. Also some numerical simulations for supporting the theoretical are given.

Submitted February 6, 2007. Published May 22, 2007.
Math Subject Classifications: 34K13, 34K18, 34K20.
Key Words: SIS model; delay; Hopf bifurcation; stability; periodic solution.

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Li Liu
School of Mathematical Sciences
South China Normal University
Guangzhou 510631, China
email: liuli_0926@163.com
Xiangao Li
School of Mathematical Sciences
South China Normal University
Guangzhou 510631, China
email: lixg@scnu.edu.cn
Kejun Zhuang
School of Mathematical Sciences
South China Normal University
Guangzhou 510631, China
email: zhkj123@163.com

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