Analysis of stability and Hopf bifurcation for an eco-epidemiological model with distributed delay | Zendy

Xueyong Zhou | Zendy; Zhen Kai Guo | Zendy

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Analysis of stability and Hopf bifurcation for an eco-epidemiological model with distributed delay

Author(s) -

Xueyong Zhou,

Zhen Kai Guo

Publication year - 2012

Publication title -

electronic journal of qualitative theory of differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.524

H-Index - 33

ISSN - 1417-3875

DOI - 10.14232/ejqtde.2012.1.44

Subject(s) - hopf bifurcation , mathematics , stability (learning theory) , bifurcation , computer science , nonlinear system , physics , quantum mechanics , machine learning

In this paper, the dynamical behavior of an eco-epidemiological model with distributed delay is studied. Sufficient conditions forthe asymptotical stability of all the equilibria are obtained. We prove that there exists a threshold value of the infection rate b beyond which the positive equilibrium bifurcates towards a periodic solution. We further analyze the orbital stability of the periodic orbits arising from bi- furcation by applying Poore's condition. Numerical simulation with some hypothetical sets of data has been done to support the analytical findings.

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