Optimal Control of a Two-Patch Dengue Epidemic under Limited Resources

Abstract

Despite the ongoing preventive measures of vector control, dengue fever still presents outbreaks, and daily commuting of people also facilitates its propagation. To contain the disease spread after an outbreak has already occurred, the local healthcare authorities are compelled to perform insecticide spraying as a corrective measure of vector control, thus trying to avoid massive human infections. Several issues concerned with the practical implementation of such corrective measures can be solved from a mathematical standpoint, and the purpose of this study is to contribute to this strand of research. Using as a basis a two-patch dengue transmission ODE model, we designed the patch-dependent optimal strategies for the insecticide spraying with the optimal control approach. We also analyzed the response of the optimal strategies to three alternative modes of budget cuts under different intensities of daily commuting. Our approach illustrated that trying “to save money” by reducing the budget for corrective control is completely unwise, and the anticipated “savings” will actually turn into considerable additional public spending for treating human infections, which could have been averted by a timely corrective intervention.