  This paper is devoted to the study of optimal release strategies to control
vector-borne diseases, such as dengue, Zika, chikungunya and malaria. Two
techniques are considered: the sterile insect one (SIT), which consists in
releasing sterilized males among wild vectors in order to perturb their
reproduction, and the Wolbachia one (presently used mainly for mosquitoes),
which consists in releasing vectors, that are infected with a bacterium
limiting their vector capacity, in order to replace the wild population by one
with reduced vector capacity. In each case, the time dynamics of the vector
population is modeled by a system of ordinary differential equations in which
the releases are represented by linear combinations of Dirac measures with
positive coefficients determining their intensity. We introduce optimal control
problems that we solve numerically using ad-hoc algorithms, based on writing
first-order optimality conditions characterizing the best combination of Dirac
measures. We then discuss the results obtained, focusing in particular on the
complexity and efficiency of optimal controls and comparing the strategies
obtained. Mathematical modeling can help testing a great number of scenarios
that are potentially interesting in future interventions (even those that are
orthogonal to the present strategies) but that would be hard, costly or even
impossible to test in the field in present conditions.
