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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 727818, 10 pages
http://dx.doi.org/10.1155/2014/727818
Research Article

Stability and Bifurcation Analysis on an Ecoepidemiological Model with Stage Structure and Time Delay

1School of Mathematics and Statistics, Hebei University of Economics & Business, Shijiazhuang 050061, China
2Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China

Received 15 April 2014; Accepted 21 July 2014; Published 12 August 2014

Academic Editor: Sanling Yuan

Copyright © 2014 Lingshu Wang and Guanghui Feng. 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

An ecoepidemiological predator-prey model with stage structure for the predator and time delay due to the gestation of the predator is investigated. The effects of a prey refuge with disease in the prey population are concerned. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the model is discussed. Further, it is proved that the model undergoes a Hopf bifurcation at the positive equilibrium. By means of appropriate Lyapunov functions and LaSalle’s invariance principle, sufficient conditions are obtained for the global stability of the semitrivial boundary equilibria. By using an iteration technique, sufficient conditions are derived for the global attractiveness of the positive equilibrium.