  In this article, we are interested in the analysis and simulation of
solutions to an optimal control problem motivated by population dynamics
issues. In order to control the spread of mosquito-borne arboviruses, the
population replacement technique consists in releasing into the environment
mosquitoes infected with the Wolbachia bacterium, which greatly reduces the
transmission of the virus to the humans. Spatial releases are then sought in
such a way that the infected mosquito population invades the uninfected
mosquito population. Assuming very high mosquito fecundity rates, we first
introduce an asymptotic model on the proportion of infected mosquitoes and then
an optimal control problem to determine the best spatial strategy to achieve
these releases. We then analyze this problem, including the optimality of
natural candidates and carry out first numerical simulations in one dimension
of space to illustrate the relevance of our approach.
