Vol. 7, No. 4, 2014

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ISSN: 1944-4184 (e-only)
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Discrete time optimal control applied to pest control problems

Wandi Ding, Raymond Hendon, Brandon Cathey, Evan Lancaster and Robert Germick

Vol. 7 (2014), No. 4, 479–489
Abstract

We apply discrete time optimal control theory to the mathematical modeling of pest control. Two scenarios: biological control and the combination of pesticide and biological control are considered. The goal is maximizing the “valuable” population, minimizing the pest population and the cost to apply the control strategies. Using the extension of Pontryagin’s maximum principle to discrete system, the adjoint systems and the characterization of the optimal pest controls are derived. Numerical simulations of various cases are provided to show the effectiveness of our methods.

Keywords
optimal control, biological pest control, discrete model, pesticide
Mathematical Subject Classification 2010
Primary: 39A10, 49K99, 92D25
Milestones
Received: 5 October 2012
Revised: 11 November 2013
Accepted: 20 December 2013
Published: 31 May 2014

Communicated by Suzanne Lenhart
Authors
Wandi Ding
Department of Mathematical Sciences
Middle Tennessee State University
Murfreesboro, TN 37132
United States
Raymond Hendon
Computational Science Program
Middle Tennessee State University
Murfreesboro, TN 37132
United States
Brandon Cathey
Department of Physics and Astronomy
University of Tennessee, Knoxville
Knoxville, TN 37996
United States
Evan Lancaster
Department of University Studies
Middle Tennessee State University
Murfreesboro, TN 37132
United States
Robert Germick
Department of Electrical Engineering
University of Tennessee
Knoxville, TN 37996
United States