Optimal releases for population replacement strategies, application to Wolbachia

Abstract : In this article, we consider a simplified model of time dynamics for a mosquito population subject to the artificial introduction of Wolbachia-infected mosquitoes, in order to fight arbovirus transmission. Indeed, it has been observed that when some mosquito populations are infected by certain Wolbachia strains, various reproductive alterations are induced in mosquitoes, including cytoplasmic incompatibility. Moreover, these Wolbachia bacteria can reduce the ability of insects to become infected by viruses such as the dengue ones, cutting down their vector competence and thus effectively stopping local dengue transmission. The behavior of infected and uninfected mosquitoes is assumed to be driven by a com-partmental system enriched with the presence of an internal control source term standing for releases of infected mosquitoes, distributed in time. We model and design an optimal release control strategy with the help of a least square problem. In a nutshell, one wants to minimize the number of uninfected mosquitoes at a given time horizon, under relevant biological constraints. We derive properties of optimal controls and study a limit problem providing useful asymptotic properties of optimal controls. We numerically illustrate the relevance of our approach.
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Submitted on : Tuesday, June 5, 2018 - 12:47:25 AM
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Luís Almeida, Yannick Privat, Martin Strugarek, Nicolas Vauchelet. Optimal releases for population replacement strategies, application to Wolbachia. 2018. ⟨hal-01807624⟩

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