Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Optimal control of integrodifference equations in a pest-pathogen system

Pages: 1759 - 1783, Volume 20, Issue 6, August 2015      doi:10.3934/dcdsb.2015.20.1759

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Marco V. Martinez - Department of Mathematics, North Central College, Naperville, IL 60540, United States (email)
Suzanne Lenhart - Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, United States (email)
K. A. Jane White - Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, United Kingdom (email)

Abstract: We develop the theory of optimal control for a system of integrodifference equations modelling a pest-pathogen system. Integrodifference equations incorporate continuous space into a system of discrete time equations. We design an objective functional to minimize the damaged cost generated by an invasive species and the cost of controlling the population with a pathogen. Existence, characterization, and uniqueness results for the optimal control and corresponding states have been completed. We use a forward-backward sweep numerical method to implement our optimization which produces spatio-temporal control strategies for the gypsy moth case study.

Keywords:  Integrodifference equations, pest-pathogen, optimal control, invasive species.
Mathematics Subject Classification:  Primary: 49J21, 92D30; Secondary: 92D40.

Received: October 2013;      Revised: November 2013;      Available Online: June 2015.