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

TL;DR

This paper develops a feedback control strategy for a reaction-diffusion model of pest populations, specifically mosquitoes, to achieve long-term extinction stabilization using the sterile insect technique.

Contribution

It extends a temporal SIT model to a spatial reaction-diffusion framework and designs a feedback law ensuring global asymptotic stability of pest extinction.

Findings

Existence and uniqueness of solutions for the spatial SIT model.

A feedback law that guarantees pest population extinction.

Robust long-term stabilization of pest populations.

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 [2], 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.