Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 392852, 15 pages
doi:10.1155/2009/392852
Research Article

Dynamics of a Stage Structure Pest Control Model with Impulsive Effects at Different Fixed Time

Bing Liu,1 Ying Duan,2 and Yinghui Gao3

1Department of Mathematics, Anshan Normal University, Anshan, Liaoning 114007, China
2Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, China
3School of Mathematics and System Sciences & LMIB, Beihang University, Beijing, 100083, China

Received 29 September 2009; Accepted 16 November 2009

Academic Editor: Leonid Berezansky

Copyright © 2009 Bing Liu 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

Many existing pest control models, which control pests by releasing natural enemies, neglect the effect that natural enemies may get killed. From this point of view, we formulate a pest control model with stage structure for the pest with constant maturation time delay (through-stage time delay) and periodic releasing natural enemies and natural enemies killed at different fixed time and perform a systematic mathematical and ecological study. By using the comparison theorem and analysis method, we obtain the conditions for the global attractivity of the pest-eradication periodic solution and permanence of the system. We also present a pest management strategy in which the pest population is kept under the economic threshold level (ETL) when the pest population is uniformly permanent. We show that maturation time delay, impulsive releasing, and killing natural enemies can bring great effects on the dynamics of the system. Numerical simulations confirm our theoretical results.