Global Stability of an Eco-Epidemiological Model with Time Delay and Saturation Incidence | Zendy

Shuxue Mao | Zendy; Rui Xu | Zendy; Zhe Li | Zendy; Yunfei Li | Zendy

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Global Stability of an Eco-Epidemiological Model with Time Delay and Saturation Incidence

Author(s) -

Shuxue Mao,

Rui Xu,

Zhe Li,

Yunfei Li

Publication year - 2011

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2011/730783

Subject(s) - hopf bifurcation , saturation (graph theory) , stability (learning theory) , mathematics , incidence (geometry) , bifurcation , sequence (biology) , computer science , combinatorics , nonlinear system , physics , chemistry , geometry , quantum mechanics , machine learning , biochemistry

We investigate a delayed eco-epidemiological model with disease in predator and saturation incidence. First, by comparison arguments, the permanence of the model is discussed. Then, we study the local stability of each equilibrium of the model by analyzing the corresponding characteristic equations and find that Hopf bifurcation occurs when the delay τ passes through a sequence of critical values. Next, by means of an iteration technique, sufficient conditions are derived for the global stability of the disease-free planar equilibrium and the positive equilibrium. Numerical examples are carried out to illustrate the analytical results

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