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Abstract and Applied Analysis
Volume 2014, Article ID 242410, 7 pages
http://dx.doi.org/10.1155/2014/242410
Research Article

Global Hopf Bifurcation Analysis for an Avian Influenza Virus Propagation Model with Nonlinear Incidence Rate and Delay

School of Science, Tianjin Polytechnic University, Tianjin 300387, China

Received 1 January 2014; Accepted 14 June 2014; Published 14 July 2014

Academic Editor: Zhichun Yang

Copyright © 2014 Yanhui Zhai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The paper investigated an avian influenza virus propagation model with nonlinear incidence rate and delay based on SIR epidemic model. We regard delay as bifurcating parameter to study the dynamical behaviors. At first, local asymptotical stability and existence of Hopf bifurcation are studied; Hopf bifurcation occurs when time delay passes through a sequence of critical values. An explicit algorithm for determining the direction of the Hopf bifurcations and stability of the bifurcation periodic solutions is derived by applying the normal form theory and center manifold theorem. What is more, the global existence of periodic solutions is established by using a global Hopf bifurcation result.