Vector-borne disease outbreak control via instant releases

TL;DR

This paper develops and analyzes optimal control strategies for vector-borne disease outbreak management using sterile insect techniques and Wolbachia-infected vectors, modeled through differential equations and optimized via numerical algorithms.

Contribution

It introduces a novel optimal control framework for release strategies, combining mathematical modeling with numerical solutions to improve disease vector management.

Findings

Optimal release strategies are characterized by Dirac measures with optimized intensities.

Numerical algorithms effectively identify efficient control measures.

Mathematical modeling enables testing of diverse intervention scenarios.

Abstract

This paper is devoted to the study of optimal release strategies to control vector-borne diseases, such as dengue, Zika, chikungunya and malaria. Two techniques are considered: the sterile insect one (SIT), which consists in releasing sterilized males among wild vectors in order to perturb their reproduction, and the Wolbachia one (presently used mainly for mosquitoes), which consists in releasing vectors, that are infected with a bacterium limiting their vector capacity, in order to replace the wild population by one with reduced vector capacity. In each case, the time dynamics of the vector population is modeled by a system of ordinary differential equations in which the releases are represented by linear combinations of Dirac measures with positive coefficients determining their intensity. We introduce optimal control problems that we solve numerically using ad-hoc algorithms, based on writing first-order optimality conditions characterizing the best combination of Dirac measures. We then discuss the results obtained, focusing in particular on the complexity and efficiency of optimal controls and comparing the strategies obtained. Mathematical modeling can help testing a great number of scenarios that are potentially interesting in future interventions (even those that are orthogonal to the present strategies) but that would be hard, costly or even impossible to test in the field in present conditions.