Optimal control of integrodifference equations in a pest-pathogen system

Marco V.  Martinez; Suzanne Lenhart; K. A. Jane  White

doi:10.3934/dcdsb.2015.20.1759

Article Contents

2015, Volume 20, Issue 6: 1759-1783. Doi: 10.3934/dcdsb.2015.20.1759 open access

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Optimal control of integrodifference equations in a pest-pathogen system

1.
Department of Mathematics, North Central College, Naperville, IL 60540
2.
Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300
3.
Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY

Received: October 2013

Revised: November 2013

Published: August 2015

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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.

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Mathematics Subject Classification: Primary: 49J21, 92D30; Secondary: 92D40.

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