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

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...

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Bibliographic Details
Published in:Discrete Dynamics in Nature and Society 2011-01, Vol.2011 (2011), p.1347-1368
Main Authors: Mao, Shuxue, Xu, Rui, Li, Zhe, Li, Yunfei
Format: Article
Language:English
Subjects:
Bifurcation theory
Computational biology
Epidemiology
Mathematical models
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Summary: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.
ISSN:1026-0226
1607-887X
DOI:10.1155/2011/730783