Abstract and Applied Analysis

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

Yanhui Zhai, Ying Xiong, Xiaona Ma, and Haiyun Bai

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 242410, 7 pages.

Dates
First available in Project Euclid: 3 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412360628

Digital Object Identifier
doi:10.1155/2014/242410

Mathematical Reviews number (MathSciNet)
MR3240528

Zentralblatt MATH identifier
07021984

Citation

Zhai, Yanhui; Xiong, Ying; Ma, Xiaona; Bai, Haiyun. Global Hopf Bifurcation Analysis for an Avian Influenza Virus Propagation Model with Nonlinear Incidence Rate and Delay. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 242410, 7 pages. doi:10.1155/2014/242410. https://projecteuclid.org/euclid.aaa/1412360628


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