[Paper Review] On the use of Traveling Waves for Pest/Vector elimination using the Sterile Insect Technique

Roumen Anguelov, Yves Dumont+1 more|arXiv (Cornell University)|Oct 2, 2020

Insect behavior and control techniques29 references4 citations

TL;DR

This paper extends a temporal Sterile Insect Technique (SIT) model to a spatially explicit, partially degenerate reaction-diffusion system to study traveling wave dynamics in pest/vector control. It proves the existence of mono-stable and bi-stable traveling waves and demonstrates that a corridor strategy—using massive releases in a spatial corridor and small releases ahead—can block and even push back invasive pest fronts, offering a sustainable, spatially targeted SIT strategy.

ABSTRACT

The development of sustainable vector/pest control methods is of utmost importance to reduce the risk of vector-borne diseases and pest damages on crops. Among them, the Sterile Insect Technique (SIT) is a very promising one. In this paper, using diffusion operators, we extend a temporal SIT model, developed in a recent paper, into a partially degenerate reaction-diffusion SIT model. Adapting some theoretical results on traveling wave solutions for partially degenerate reaction-diffusion equations, we show the existence of mono-stable and bi-stable traveling-wave solutions for our SIT system. The dynamics of our system is driven by a SIT-threshold number above which the SIT control becomes effective and drives the system to elimination, using massive releases. When the amount of sterile males is lower than the SIT-threshold, the SIT model experiences a strong Allee effect such that a bi-stable traveling wave solution can exist and can also be used to derive an effective long term strategy, mixing massive and small releases. We illustrate some of our theoretical results with numerical simulations , and, also explore numerically spatial-localized SIT control strategies, using massive and small releases. We show that this "corridor" strategy can be efficient to block an invasion and eventually can be used to push back the front of a vector/pest invasion.

Motivation & Objective

• To extend a temporal SIT model to a spatio-temporal reaction-diffusion framework that accounts for adult dispersal of pests/vectors.
• To investigate the existence and properties of traveling wave solutions in a partially degenerate reaction-diffusion SIT system.
• To develop and evaluate spatially targeted SIT control strategies, particularly corridor and barrier approaches, for blocking and reversing pest invasions.
• To provide theoretical and numerical support for optimizing SIT release protocols in real-world applications, especially in regions like La Réunion and Corsica.
• To address the challenge of SIT failure in large-scale deployments by introducing dynamic, localized release strategies based on wave dynamics.

Proposed method

• Formulates a partially degenerate reaction-diffusion system to model the spatio-temporal dynamics of wild and sterile male insects.
• Applies theoretical results on traveling wave solutions for degenerate reaction-diffusion equations to analyze wave existence and stability.
• Introduces a SIT-threshold parameter $ M_{T_1} $, above which the system drives populations to elimination via massive releases.
• Designs a 'corridor strategy' with spatially localized massive releases to block invasion fronts and small releases ahead to maintain suppression.
• Uses numerical simulations to validate wave behavior and assess the efficiency of corridor-based control under varying release intensities and diffusion rates.
• Employs parameters from real-world SIT projects (e.g., Aedes albopictus in La Réunion, Ceratitis capitata in Corsica) to ensure ecological relevance.

Experimental results

Research questions

• RQ1 Under what conditions does a traveling wave solution exist in a spatially extended SIT model with partial degeneracy?
• RQ2 How does the SIT-threshold $ M_{T_1} $ influence the existence of mono-stable versus bi-stable traveling waves?
• RQ3 Can a corridor-based release strategy effectively block and reverse an invading pest or vector front?
• RQ4 What is the role of the Allee effect in enabling bi-stable wave dynamics and long-term control with small releases?
• RQ5 How do diffusion rates and release intensities affect the success of spatially localized SIT interventions?

Key findings

• The model proves the existence of both mono-stable and bi-stable traveling wave solutions in a partially degenerate reaction-diffusion SIT system.
• When $ M_T < M_{T_1} $, a monotone wavefront connects the disease-free state (0) to a positive equilibrium, indicating population persistence.
• When $ M_T > M_{T_1} $, numerical simulations confirm that the system can be driven to complete elimination via massive releases.
• The corridor strategy—using massive releases in a 27 km or 40 km wide corridor and small releases ahead—successfully blocks and pushes back the invasion front.
• With $ M_T = 1.8 imes M_{T_1} $, $ d_M = 0.05 $, $ d_F = 0.1 $, and $ ho = 0.08 $, simulations show effective wave blocking and reversal over time.
• The corridor strategy is theoretically extendable to other pests such as Ceratitis capitata and Bactrocera dorsalis, with real-world analogs like the medfly barrier in Central America.