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Minimal cost-time strategies for population replacement using the IIT

Almeida, Luis; Bellver, Jesús; Duprez, Michel; Privat, Yannick (2020), Minimal cost-time strategies for population replacement using the IIT. https://basepub.dauphine.fr/handle/123456789/20612

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duprez.pdf (473.6Kb)
Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02532677
Date
2020
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
15
Metadata
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Author(s)
Almeida, Luis cc
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Bellver, Jesús
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Duprez, Michel cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Privat, Yannick cc
Institut de Recherche Mathématique Avancée [IRMA]
Abstract (EN)
Vector control plays a central role in the fight against vector-borne diseases and, in particular, arboviruses. The use of the endosymbiotic bacterium Wolbachia has proven effective in preventing the transmission of some of these viruses between mosquitoes and humans, making it a promising control tool. The Incompatible Insect Technique (IIT) consists in replacing the wild population by a population carrying the aforementioned bacterium, thereby preventing outbreaks of the associated vector-borne diseases. In this work, we consider a two species model incorporating both Wolbachia infected and wild mosquitoes. Our system can be controlled thanks to a term representing an artificial introduction of Wolbachia-infected mosquitoes. Under the assumption that the birth rate of mosquitoes is high, we may reduce the model to a simpler one on the proportion of infected mosquitoes. We investigate minimal cost-time strategies to achieve a population replacement both analytically and numerically for the simplified 1D model and only numerically for the full 2D system
Subjects / Keywords
Wolbachia; ordinary differential systems; optimal control; minimal time

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