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In this article, we are interested in the analysis and simulation ofsolutions to an optimal control problem motivated by population dynamicsissues. In order to control the spread of mosquito-borne arboviruses, thepopulation replacement technique consists in releasing into the environmentmosquitoes infected with the Wolbachia bacterium, which greatly reduces thetransmission of the virus to the humans. Spatial releases are then sought insuch a way that the infected mosquito population invades the uninfectedmosquito population. Assuming very high mosquito fecundity rates, we firstintroduce an asymptotic model on the proportion of infected mosquitoes and thenan optimal control problem to determine the best spatial strategy to achievethese releases. We then analyze this problem, including the optimality ofnatural candidates and carry out first numerical simulations in one dimensionof space to illustrate the relevance of our approach.

Optimization of spatial control strategies for population replacement, application to Wolbachia