Optimal control strategies for bistable ODE equations: Application to mosquito population replacement - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Applied Mathematics and Optimization Année : 2022

Optimal control strategies for bistable ODE equations: Application to mosquito population replacement

Résumé

Vector-borne diseases, in particular arboviruses, represent a major threat to human health. In the fight against these viruses, the endosymbiotic bacterium Wolbachia has become in recent years a promising tool as it has been shown to prevent the transmission of some of these viruses between mosquitoes and humans. In this work, we investigate optimal population replacement strategies, which consists in replacing optimally the wild population by a population carrying the aforementioned bacterium, making less likely the appearance of outbreaks of these diseases. We consider a two species model taking into account both wild and Wolbachia infected mosquitoes. To control the system, we introduce a term representing an artificial introduction of Wolbachia-infected mosquitoes. Assuming a high birth rate, we reduce the model to a simpler one regarding the proportion of infected mosquitoes. We study strategies optimizing a convex combination either of cost and time or cost and final proportion of mosquitoes in the population. We fully analyze each of the introduced problem families, proving a time monotonicity property on the proportion of infected mosquitoes and using a reformulation of the problem based on a suitable change of variable. Our results are useful in considerably more general contexts which we present.
Fichier principal
Vignette du fichier
articleABP.pdf (701.99 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03212761 , version 1 (29-04-2021)
hal-03212761 , version 2 (27-12-2022)

Identifiants

  • HAL Id : hal-03212761 , version 2

Citer

Luis Almeida, Jesús Bellver Arnau, Yannick Privat. Optimal control strategies for bistable ODE equations: Application to mosquito population replacement. Applied Mathematics and Optimization, 2022. ⟨hal-03212761v2⟩
195 Consultations
153 Téléchargements

Partager

Gmail Facebook X LinkedIn More