Optimal strategies for Wolbachia mosquito replacement technique: influence of the carrying capacity on spatial releases

¹ Sorbonne Université, CNRS, Université de Paris, Inria, Laboratoire J.-L. Lions, 75005 Paris, France.
² Université Sorbonne Paris Nord, Laboratoire Analyse, Géométrie et Applications, LAGA, CNRS UMR 7539, 93430 Villetaneuse, France.

^* Corresponding author: jesus.bellver@ceab.csic.es
^a Current address: Centre d’Estudis Avançats de Blanes (CEAB-CSIC), Carrer d’Accés a la cala Sant Francesc 14, 17300 Blanes, Spain.

Received: 1 September 2023
Accepted: 5 May 2025

Abstract

This work is devoted to the mathematical study of an optimization problem regarding control strategies of mosquito population in a heterogeneous environment. Mosquitoes are well-known vectors of diseases. For some diseases, such as dengue, it has been found that mosquitoes have a reduced vector capacity when carrying the endosymbiotic bacterium Wolbachia. We consider a mathematical model of a replacement technique consisting in rearing and releasing Wolbachia-infected mosquitoes to replace the wild population. Our goal is to optimize the release protocol to maximize replacement effectiveness in a spatially inhomogeneous environment. Using a scalar model with space-dependent carrying capacity, we explore the existence and properties of an optimal single-release profile at initial time maximizing the replacement across the domain. In particular, neglecting mosquito mobility and under some assumptions on the biological parameters, we characterize the optimal releasing strategy for a short time horizon, and we reduce the case of a long time horizon to a one-dimensional optimization problem. Our theoretical results are illustrated with several numerical simulations.