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

Alexis Léculier (1, 2) , Nga Nguyen (3, 4, 1)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 UB - Université de Bordeaux
3 LAGA - Laboratoire Analyse, Géométrie et Applications
4 MAMBA - Modelling and Analysis for Medical and Biological Applications

In this paper, we introduce a control strategy for applying the Sterile Insect Technique (SIT) to eliminate the population of Aedes mosquitoes 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-called hair-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 speed c to 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.

Mots clés: sterile insect technique; hair-trigger effect; traveling waves; sterile insect technique hair-trigger effect traveling waves; sterile insect technique

Domaines: Equations aux dérivées partielles [math.AP]; Evolution [q-bio.PE]

Alexis Léculier, Nga Nguyen. A control strategy for Sterile Insect Techniques using exponentially decreasing releases to avoid the hair-trigger effect. 2023. ⟨hal-03851525v2⟩