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Discrete Dynamics in Nature and Society
Volume 2011, Article ID 730783, 22 pages
http://dx.doi.org/10.1155/2011/730783
Research Article

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

Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China

Received 30 June 2011; Accepted 23 August 2011

Academic Editor: Her-Terng Yau

Copyright © 2011 Shuxue Mao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 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.