[Paper Review] Control strategies on mosquitos population for the fight against arboviruses

Luís Almeida, Michel Duprez+2 more|arXiv (Cornell University)|Jan 17, 2019

Insect symbiosis and bacterial influences18 references4 citations

TL;DR

This paper formulates and solves optimal control problems for two mosquito-borne arbovirus control strategies—Sterile Insect Technique (SIT) and Wolbachia-mediated population replacement—using a mathematical model of mosquito population dynamics. It derives necessary optimality conditions and demonstrates through numerical simulations that temporally optimized release protocols significantly improve target outcomes, such as minimizing wild female mosquitoes or achieving Wolbachia fixation.

ABSTRACT

In the fight against vector-borne arboviruses, an important strategy of control of epidemic consists in controlling the population of vector, extit{Aedes} mosquitoes in this case. Among possible actions, two techniques consist in releasing mosquitoes to reduce the size of the population (Sterile Insect Technique) or in replacing the wild population by a population carrying a bacteria, called extit{Wolbachia}, blocking the transmission of viruses from mosquitoes to human. This paper is concerned with the question of optimizing the release protocol for these two strategies with the aim of getting as close as possible to the objectives. Starting from a mathematical model describing the dynamics of the population, we include the control function and introduce the cost functional for both extit{population replacement} and extit{Sterile Insect Technique} problems. Next, we establish some properties of the optimal control and illustrate them with some numerical simulations.

Motivation & Objective

• To design optimal release protocols for mosquito population control to reduce arbovirus transmission.
• To minimize the number of wild female mosquitoes using the Sterile Insect Technique (SIT).
• To drive the mosquito population toward a Wolbachia-infected equilibrium via population replacement.
• To account for limited total release quantities over a fixed time horizon.
• To derive and analyze the structure of optimal control functions using Pontryagin’s maximum principle.

Proposed method

• Formulates a compartmental model of mosquito life cycle including eggs, larvae, pupae, and adults, with separate compartments for wild and modified mosquitoes.
• Simplifies the full system into two tractable models: one for SIT (sterile males only) and one for Wolbachia replacement (infected males and females).
• Introduces a cost functional that minimizes the number of wild females at final time for SIT, and the L2-distance to the Wolbachia-infected equilibrium for population replacement.
• Applies optimal control theory with bounded control inputs (total release constraint), using Pontryagin’s maximum principle to derive necessary conditions for optimality.
• Derives the structure of the optimal control, showing that release rates are zero near the final time due to terminal conditions on adjoint variables.
• Performs numerical simulations to illustrate the impact of different release timing strategies on final population outcomes.

Experimental results

Research questions

• RQ1 What is the optimal temporal distribution of sterile male releases to minimize the number of wild female mosquitoes at the end of a fixed intervention period?
• RQ2 How should Wolbachia-infected mosquitoes be released over time to most closely approach the desired infected equilibrium state?
• RQ3 What mathematical structure characterizes the optimal release protocol under a total release budget constraint?
• RQ4 How do adjoint variables and the Pontryagin maximum principle shape the optimal control strategy in both SIT and population replacement?
• RQ5 What are the qualitative properties of the optimal control, such as its behavior near the final time?

Key findings

• The optimal control for the Sterile Insect Technique is zero in a neighborhood of the final time, due to the terminal condition on the adjoint variable.
• For Wolbachia population replacement, the optimal control also vanishes near the final time, indicating that late releases are inefficient.
• The adjoint variables for both problems are strictly positive in the interior of the time interval, ensuring that the optimal control is not trivial.
• Numerical simulations confirm that optimized release protocols significantly outperform uniform or naive release strategies in reaching the target population state.
• The existence of an optimal control is rigorously proven using weak compactness and lower semicontinuity arguments in Sobolev spaces.
• The system dynamics remain bounded and biologically meaningful (e.g., population levels stay positive and below carrying capacity) under optimal controls.