Feedback stabilization for a spatial-dependent Sterile Insect Technique model with Allee Effect

¹ Sorbonne Université, Université Paris Cité, CNRS, INRIA, Laboratoire Jacques-Louis Lions, LJLL, EPC, CAGE, F-75005 Paris, France
² Sorbonne Université, Université Paris Cité, CNRS, Laboratoire de Probabilités, Statistique et Modélisation, LPSM, F-75005 Paris, France

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 8 February 2025
Accepted: 2 February 2026

Abstract

This work focuses on feedback control strategies for applying the sterile insect technique (SIT) to eliminate pest populations. The presentation is centered on the case of mosquito populations, but most of the results can be extended to other species by adapting the model and selecting appropriate parameter values to describe the reproduction and movement dynamics of the species under consideration. In our study, we address the spatial distribution of the population in a two dimensional bounded domain by extending the temporal SIT model analyzed in [Agbo bidi Math. Biosci. Eng. 21 (2024) 6263–6288], thereby obtaining a reaction-diffusion SIT model. After the analysis of the existence and the uniqueness of the solution of this problem, we construct a feedback law that globally asymptotically stabilizes the extinction equilibrium thus yielding a robust strategy to keep the pest population at very low levels in the long term.