Mosquito population control strategies for fighting against arboviruses

Luís Almeida (1, 2) , Michel Duprez (1) , Yannick Privat (3, 4) , Nicolas Vauchelet (5)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 MAMBA - Modelling and Analysis for Medical and Biological Applications
3 IRMA - Institut de Recherche Mathématique Avancée
4 TONUS - TOkamaks and NUmerical Simulations
5 LAGA - Laboratoire Analyse, Géométrie et Applications

In the fight against vector-borne arboviruses, an important strategy of control of epidemic consists in controlling the population of the vector, \textit{Aedes} mosquitoes in this case. Among possible actions, two techniques consist either in releasing sterile mosquitoes to reduce the size of the population (Sterile Insect Technique) or in replacing the wild population by one carrying a bacteria, called \textit{Wolbachia}, blocking the transmission of viruses from insects to humans. This article addresses the issue of optimizing the dissemination protocol for each of these strategies, in order to get as close as possible to these objectives. Starting from a mathematical model describing population dynamics, we study the control problem and introduce the cost function standing for {\it population replacement} and {\it sterile insect technique}. Then, we establish some properties of the optimal control and illustrate them with numerical simulations.

Mots clés: Optimal control; Wolbachia; Sterile Insect technique; Modelling

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Luís Almeida, Michel Duprez, Yannick Privat, Nicolas Vauchelet. Mosquito population control strategies for fighting against arboviruses. Mathematical Biosciences and Engineering, 2019, 16 (6), pp.6274-6297. ⟨10.3934/mbe.2019313⟩. ⟨hal-01984426v2⟩