In the fight against vector-borne arboviruses, an important strategy of control of epidemic consists in controlling the population of the vector, mosquitoes in this case. Among possible actions, two techniques consist either in releasing sterile mosquitoes to reduce the size of the population (Sterile Insect Technique) or in replacing the wild population by one carrying a bacteria, called blocking the transmission of viruses from insects to humans. This article addresses the issue of optimizing the dissemination protocol for each of these strategies, in order to get as close as possible to these objectives. Starting from a mathematical model describing population dynamics, we study the control problem and introduce the cost function standing for and Then, we establish some properties of the optimal control and illustrate them with numerical simulations.
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