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.
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