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Optimal harvesting during an invasion of a sublethal plant pathogen

Published online by Cambridge University Press:  04 October 2007

HOLLY GAFF
Affiliation:
Department of Epidemiology and Preventive Medicine, University of Maryland, School of Medicine, 660 West Redwood Street, Baltimore, Maryland 21201. Email: hgaff@epi.umaryland.edu
HEM RAJ JOSHI
Affiliation:
Mathematics and Computer Science Department, Xavier University, Cincinnati, OH 45207-4441.
SUZANNE LENHART
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300.

Abstract

Plant pathogens are quite destructive to cash crops throughout the world, resulting in potentially devastating financial losses. This work expands recently developed optimal control theory for an integrodifference model to a mathematical system which includes an integrodifference component. This system models a highly simplified plant pathogen system for which the optimal harvesting scheme is derived. An adjoint system is introduced to characterize the optimal harvesting pattern. This analysis shows that, while it may not be possible to prevent losses upon discovery of the pathogen in an area, it is theoretically possible to significantly cut those losses by culling an area around the initial infection.

Type
Research Article
Copyright
2007 Cambridge University Press

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Footnotes

This work was partially supported by National Science Foundation grant DMS 0110920.
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