A control strategy for Sterile Insect Techniques using exponentially decreasing releases to avoid the hair-trigger effect

TL;DR

This paper proposes a control strategy using exponentially decreasing releases of sterile males to effectively eliminate mosquito populations and prevent invasion due to hair-trigger effects, supported by mathematical analysis and numerical simulations.

Contribution

It introduces a novel control method employing decreasing sterile insect releases and provides mathematical proof of its effectiveness against mosquito invasion.

Findings

The strategy prevents mosquito invasion with finite sterile male releases.

Mathematical analysis confirms the success of the decreasing release approach.

Numerical simulations illustrate the practical application of the method.

Abstract

In this paper, we introduce a control strategy for applying the Sterile Insect Technique (SIT) to eliminate the population of Aedes mosquitoes which are the vectors of various deadly diseases like dengue, zika, chikungunya... in a wide area. We use a system of reaction-diffusion equations to model the mosquito population and study the effect of releasing sterile males. Due to the so-called hair-trigger effects, the introduction of only a few individuals can lead to the invasion of mosquitoes in the whole region after some time. To avoid this phenomenon, our strategy is to keep releasing a small number of sterile males in the treated zone and move this release forward to push back the invasive front of wild mosquitoes. By proving a comparison principle for the system and using the traveling wave analysis, we show in the present paper that the strategy succeeds with a finite amount of sterile male mosquitoes. We also provide some numerical illustrations for our results.