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Journal of Applied Mathematics
Volume 2012, Article ID 852631, 24 pages
http://dx.doi.org/10.1155/2012/852631
Research Article

The Dynamics of an Eco-Epidemiological Model with Nonlinear Incidence Rate

1Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
2Department of Mathematics, College of Science, University of Sulaimania, Sulaimania, Iraq

Received 5 May 2012; Accepted 10 August 2012

Academic Editor: Junjie Wei

Copyright © 2012 Raid Kamel Naji and Arkan N. Mustafa. 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

This paper treats the dynamical behavior of eco-epidemiological model with nonlinear incidence rate. A Holling type II prey-predator model with SI-type of disease in prey has been proposed and analyzed. The existence, uniqueness, and boundedness of the solution of the system are studied. The local and global dynamical behaviors are investigated. The conditions, which guarantee the occurring of Hopf bifurcation of the system, are established. Finally, further investigations for the global dynamics of the proposed system are carried out with the help of numerical simulations.