Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 726783, 14 pages
Research Article

Impulsive Biological Pest Control Strategies of the Sugarcane Borer

Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas, Universidade Federal do ABC, 09.210-110 Santo André, SP, Brazil

Received 7 April 2012; Accepted 11 June 2012

Academic Editor: Alexander P. Seyranian

Copyright © 2012 Marat Rafikov 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.


We propose an impulsive biological pest control of the sugarcane borer (Diatraea saccharalis) by its egg parasitoid Trichogramma galloi based on a mathematical model in which the sugarcane borer is represented by the egg and larval stages, and the parasitoid is considered in terms of the parasitized eggs. By using the Floquet theory and the small amplitude perturbation method, we show that there exists a globally asymptotically stable pest-eradication periodic solution when some conditions hold. The numerical simulations show that the impulsive release of parasitoids provides reliable strategies of the biological pest control of the sugarcane borer.