IJPAM: Volume 91, No. 4 (2014)

HOPF BIFURCATION OF AN EPIDEMIC MODEL WITH
A NONLINEAR BIRTH IN POPULATION
AND STAGE STRUCTURE

Yinying Zhang$^1$, Jianwen Jia$^2$
School of Mathematics and Computer Science
Shanxi Normal University
Shanxi, Linfen, 041004, P.R. CHINA


Abstract. In this paper, an epidemic model involving a nonlinear birth in population and stage structure was studied. The stability of disease-free equilibrium was verified by Routh-Hurwitz criterion and LaSalle's invariance principle. We researched the existence of Hopf bifurcation and obtained the stability and direction of the Hopf bifurcation by using the normal theory and the center manifold theorem. In the end, numerical simulations were carried out to illustrate the main theoretical results and a brief discussion was given to conclude this work.

Received: December 14, 2013

AMS Subject Classification: 34C25, 34K45, 92D25

Key Words and Phrases: stage structure, Hopf bifurcation, center manifold theorem

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DOI: 10.12732/ijpam.v91i4.8 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 91
Issue: 4