Malaria modeling and optimal control using sterile insect technique and insecticide-treated net

Abstract

We investigate a malaria transmission model with SEIR (susceptible-exposed-infected-recovered) classes for the human population, SEI (susceptible-exposed-infected) classes for the wild mosquitoes and an additional class for the sterile mosquitoes. The basic reproduction number of the disease transmission is obtained, and a release threshold of the sterile mosquitoes is provided. We formulate an optimal control problem in which the goal is to minimize both the infected human populations and the cost to implement two control strategies: the release of sterile mosquitoes and the usage of insecticide-treated nets to reduce the malaria transmission. Adjoint equations are derived, and the characterization of the optimal controls is established. Finally, we quantify the effectiveness of the two interventions aimed at limiting the spread of malaria transmission. A combination of both strategies leads to more rapid elimination of the wild mosquito population that can suppress malaria transmission. Numerical simulations are provided to illustrate the results.