Optimal control of disease infestations on a lattice

The design of durable and sustainable strategies for the control of plant diseases is not possible without due consideration of landscape structure and economic factors. However, many studies on control strategies of plant infestation have overlooked these considerations. In this paper, we address the problem of how best to deploy resources for the control of disease outbreaks during a single agricultural season. We consider a spatial model for the spread of a plant pathogen over an agricultural region, and model the effect of control on disease dynamics. We associate with a control strategy a 'costs function' that balances amount invested for treatment to the cost incurred by disease infestation. Our objective is to minimize the level of disease infestation and the effort of control. We prove the existence of a solution to the optimal control problem, and devise a numerical algorithm to compute it. We present results of our numerical studies, and show that the solution depends on the interplay between economic and epidemiological factors, as well as the nature of the control agent.