Modeling the impact of sterile males on an Aedes aegypti population with optimal control

We use partial differential equations to describe the dynamics of an Aedes aegypti mosquito population on an island, and the effects of a sterile male release. The model includes mosquito movement and an Allee effect to capture extinction events. We apply optimal control theory to identify the release strategy that eliminates the mosquitoes most rapidly, conditional on a limited availability of sterile males. The optimal solution for a single location is to initially release a substantial number of mosquitoes and to subsequently release fewer sterile males proportionally to the decreasing female population. The optimal solution for the whole island is intractable given a constraint on the total daily release of sterile males. The best approximation to the spatial optimal control strategy is to focus on the high mosquito density areas first and then move outwards (in both directions along the periphery of the island), until all areas have been covered, retaining throughout sufficient release intensity to prevent reintroduction in the already cleared areas.