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International Journal of Differential Equations
Volume 2017, Article ID 1820607, 18 pages
https://doi.org/10.1155/2017/1820607
Research Article

Modeling and Analysis of Integrated Pest Control Strategies via Impulsive Differential Equations

1Center for Applied Dynamical Systems and Computational Methods (CADSCOM), Faculty of Natural Sciences and Mathematics, Escuela Superior Politécnica del Litoral, P.O. Box 09-01-5863, Guayaquil, Ecuador
2Center for Dynamics, Department of Mathematics, TU Dresden, 01062 Dresden, Germany
3Institute of Hydrobiology, Faculty of Environmental Sciences, TU Dresden, 01062 Dresden, Germany

Correspondence should be addressed to Joseph Páez Chávez; ce.ude.lopse@zeapj

Received 2 August 2017; Accepted 6 November 2017; Published 3 December 2017

Academic Editor: Guodong Zhang

Copyright © 2017 Joseph Páez Chávez 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

The paper is concerned with the development and numerical analysis of mathematical models used to describe complex biological systems in the framework of Integrated Pest Management (IPM). Established in the late 1950s, IPM is a pest management paradigm that involves the combination of different pest control methods in ways that complement one another, so as to reduce excessive use of pesticides and minimize environmental impact. Since the introduction of the IPM concept, a rich set of mathematical models has emerged, and the present work discusses the development in this area in recent years. Furthermore, a comprehensive parametric study of an IPM-based impulsive control scheme is carried out via path-following techniques. The analysis addresses practical questions, such as how to determine the parameter values of the system yielding an optimal pest control, in terms of operation costs and environmental damage. The numerical study concludes with an exploration of the dynamical features of the impulsive model, which reveals the presence of codimension-1 bifurcations of limit cycles, hysteretic effects, and period-doubling cascades, which is a precursor to the onset of chaos.