Abstract and Applied Analysis
Volume 2013 (2013), Article ID 424723, 13 pages
http://dx.doi.org/10.1155/2013/424723
Research Article

Two Generalized Predator-Prey Models for Integrated Pest Management with Stage Structure and Disease in the Prey Population

Ruiqing Shi,1,2 Sanyi Tang,1 and Wenli Feng2

1College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, Shaanxi 710062, China
2School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, China

Received 22 November 2012; Accepted 17 December 2012

Academic Editor: Jinhu Lü

Copyright © 2013 Ruiqing 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

Stage-structured predator-prey models with disease in the prey are constructed. For the purpose of integrated pest management, two types of impulsive control strategies (impulsive release of infective prey and impulsive release of predator) are used. For Case  1, infective prey applications are more frequent than releases of predator (natural enemies). For Case  2, predator (natural enemies) releases are more frequent than infective prey applications. In both cases, we get the sufficient conditions for the global attractivity of the susceptible prey-eradication periodic solution. In addition, the persistence of the systems is also discussed. At last, the results are discussed and some possible future work is put forward.