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

TL;DR

This paper mathematically investigates optimal Wolbachia-infected mosquito release strategies in spatially heterogeneous environments to maximize population replacement, considering the influence of carrying capacity and release timing.

Contribution

It introduces a mathematical framework for optimizing mosquito release protocols in inhomogeneous environments, including existence and characterization of optimal strategies.

Findings

Optimal release strategies depend on spatial carrying capacity.

Short-term optimal strategies are characterized analytically.

Numerical simulations illustrate the theoretical results.

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 release profile 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.