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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 486463, 15 pages
http://dx.doi.org/10.1155/2015/486463
Research Article

Almost Periodic Solution for an Epidemic Prey-Predator System with Impulsive Effects and Multiple Delays

School of Science, Southwest University of Science and Technology, Mianyang 621010, China

Received 28 March 2015; Accepted 16 August 2015

Academic Editor: Mauro Sodini

Copyright © 2015 Baodan Tian 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 nonautonomous epidemic prey-predator system with impulsive effects and multiple delays is considered; further, there is an epidemic disease in the predator. By the mean-value theorem of multiple variables, integral inequalities, differential inequalities, and other mathematical analysis skills, sufficient conditions which guarantee the permanence of the system are obtained. Furthermore, by constructing a series of Lyapunov functionals it is proved that there exists a unique uniformly asymptotically stable almost periodic solution of the system.