A control strategy for the sterile insect technique using exponentially decreasing releases to avoid the hair-trigger effect

Abstract

In this paper, we introduce a control strategy for applying the Sterile Insect Technique (SIT) to eliminate the population ofAedesmosquitoes which are 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. Without any human intervention, and due to the so-calledhair-trigger effect, the introduction of only a few individuals (eggs or fertilized females) 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 with a negative forcing speedcto push back the invasive front of wild mosquitoes. By using traveling wave analysis, we show in the present paper that the strategy succeeds in repulsing the population while consuming a finite amount of mosquitoes in any finite time interval even though we treat a moving half-space {x>ct}. Moreover, we succeed in constructing a ‘forced’ traveling wave for our system moving at the same speed as the releases. We also provide some numerical illustrations for our results.