Optimal control of insects through sterile insect release and habitat modification

•Introduction of sterile mosquitoes and reduction of egg maturation are considered.•We apply optimal control techniques with a view to reducing the population of wild mosquitoes.•An optimal strategy can be determined for a particular mosquito population.•Simulations show bounds on sterile mosquito release and egg maturation are significant factors. This paper develops an optimal control framework for an ordinary differential equation model to investigate the introduction of sterile mosquitoes to reduce the incidence of mosquito-borne diseases. Existence of a solution given an optimal strategy and the optimal control is determined in association with the negative effects of the disease on the population while minimizing the cost due to this control mechanism. Numerical simulations have shown the importance of effects of the bounds on the release of sterile mosquitoes and the bounds on the likelihood of egg maturation. The optimal strategy is to maximize the use of habitat modification or insecticide. A combination of techniques leads to a more rapid elimination of the wild mosquito population.