Optimizing the control of disease infestations at the landscape scale

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Abstract
Using a contact-process model for the spread of crop disease over a regional scale, we examine the importance of the time scale for control with respect to the cost of the epidemic. The costs include the direct cost of treating infected sites as well as the indirect costs incurred through lost yield. We first use a mean-field approximation to derive analytical results for the optimal treatment regimes that minimize the total cost of the epidemic. We distinguish short- and long-term epidemics. and show that seasonal control (short time scale) requires extreme treatment, either treating all sites or none or switching between the two at some stage during the season. The optimal long-term strategy requires an intermediate level of control that results in near eradication of the disease. We also demonstrate the importance of incorporating economic constraints by deriving a critical relationship between the epidemiological and economic parameters that determine the qualitative nature of the optimal treatment strategy. The set of optimal strategies is summarized in a policy plot, which can be used to determine the nature of the optimal treatment regime given prior knowledge of the epidemiological and economic parameters. Finally, we test the robustness of the analytical results, derived from the mean-field approximation, on the spatially explicit contact process and demonstrate robustness to implementation errors and misestimation of crucial parameters.