# Implementation of Control Strategies for Sterile Insect Techniques

## TL;DR

This paper develops and analyzes control strategies for eliminating wild mosquito populations using sterile insect techniques, focusing on open-loop, closed-loop, and mixed impulsive release methods with proven convergence conditions.

## Contribution

It introduces a comprehensive mathematical framework for designing and analyzing both open-loop and closed-loop control strategies for sterile insect releases, including a novel mixed approach.

## Key findings

- Global convergence to mosquito-free state under specified conditions.
- Closed-loop control adapts to real-time population estimates.
- Mixed strategy optimizes elimination time and release efficiency.

## Abstract

In this paper, we propose a sex-structured entomological model that serves as a basis for design of control strategies relying on releases of sterile male mosquitoes (Aedes spp) and aiming at elimination of the wild vector population in some target locality. We consider different types of releases (constant and periodic impulsive), providing necessary conditions to reach elimination. However, the main part of the paper is focused on the study of the periodic impulsive control in different situations. When the size of wild mosquito population cannot be assessed in real time, we propose the so-called open-loop control strategy that relies on periodic impulsive releases of sterile males with constant release size. Under this control mode, global convergence towards the mosquito-free equilibrium is proved on the grounds of sufficient condition that relates the size and frequency of releases. If periodic assessments (either synchronized with releases or more sparse) of the wild population size are available in real time, we propose the so-called closed-loop control strategy, which is adjustable in accordance with reliable estimations of the wild population sizes. Under this control mode, global convergence to the mosquito-free equilibrium is proved on the grounds of another sufficient condition that relates not only the size and frequency of periodic releases but also the frequency of sparse measurements taken on wild populations. Finally, we propose a mixed control strategy that combines open-loop and closed-loop strategies. This control mode renders the best result, in terms of overall time needed to reach elimination and the number of releases to be effectively carried out during the whole release campaign, while requiring for a reasonable amount of released sterile insects.