Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 196204, 16 pages
doi:10.1155/2010/196204
Research Article

Dynamical Properties of a Delay Prey-Predator Model with Disease in the Prey Species Only

Xiangyun Shi,1 Xueyong Zhou,1,2 and Xinyu Song1

1College of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan 464000, China
2School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu 210046, China

Received 3 September 2010; Revised 11 November 2010; Accepted 17 November 2010

Academic Editor: Wei-Der Chang

Copyright © 2010 Xiangyun Shi 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

A three-dimensional ecoepidemiological model with delay is considered. We first investigate the existence and stability of the equilibria. We then study the effect of the time delay on the stability of the positive equilibrium. The existence of a Hopf bifurcation at the positive equilibrium is obtained through the study of an exponential polynomial equation with delay-dependent coefficients. Numerical simulation with a hypothetical set of data has been carried out to support the analytical findings.