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

¹ Inria, équipe Mimesis, Université de Strasbourg, Icube, 1 Place de l’Hôpital, Strasbourg, France.
² IRMA, Université de Strasbourg, CNRS UMR 7501, Inria, 7 rue René Descartes, 67084 Strasbourg, France.
³ Laboratoire Analyse, Géométrie et Applications CNRS UMR 7539, Université Sorbonne Paris Nord, Villetaneuse, France.

^* Corresponding author: yannick.privat@unistra.fr

Received: 7 December 2020
Accepted: 23 June 2021

Abstract

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.