Global Hopf bifurcation analysis for an avian influenza virus propagation model with nonlinear incidence rate and delay. (English) Zbl 1406.92639

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

Abstr. Appl. Anal. 2014, Article ID 242410, 7 p. (2014).

Summary: 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.

MSC:

92D30	Epidemiology
34C23	Bifurcation theory for ordinary differential equations
34C25	Periodic solutions to ordinary differential equations

Keywords:

avian influenza virus propagation; Hopf bifurcation; nonlinear incidence rate; periodic solution

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