Table of Contents
ISRN Applied Mathematics
Volume 2012 (2012), Article ID 598539, 14 pages
http://dx.doi.org/10.5402/2012/598539
Research Article

The Study of a Class of Pest Control Pollution Model with Stage-Structure and Time Delay

School of Mathematics and Computer Science, Shaanxi Normal University, Shanxi, Linfen 041004, China

Received 1 March 2012; Accepted 26 March 2012

Academic Editors: A. Bellouquid and C. Lu

Copyright © 2012 Jianwen Jia and Bo Wu. 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 construct a pest control pollution model with stage-structure for pests and with epidemic in the predator by spraying pesticides and releasing susceptible predators together. We assume that only the pests and infective predators are affected by pesticide. We show that there exists a globally attractive pest-extinction periodic solution and we get the condition of global attractiveness of the pest-extinction periodic solution by applying comparison theorem of impulsive differential equation. Further, the condition for the permanence of the system is also given.