Sterile Insect Technique in a n-patch system with Allee effect and mass trapping: modeling, analysis and simulations

TL;DR

This paper models the spatial dynamics of sterile insect technique (SIT) with Allee effects and mass trapping, providing conditions for population elimination, optimization of releases, and analyzing practical scenarios for pest control.

Contribution

It introduces a spatially explicit model incorporating Allee effects and mass trapping, deriving conditions for SIT success and optimizing release strategies.

Findings

Sufficient condition for wild population elimination based on Perron value.

Finite control time bounds when Allee effect is present.

Mass trapping reduces total sterile insect releases and program duration.

Abstract

The sterile insect technique (SIT) is a biological control method aimed at reducing or eliminating populations of pests or disease vectors. This technique involves releasing sterilised insects which, by mating with wild individuals, will reduce the target population. In this study, we take into account the spatial dimension by modelling the pest/vector population as being distributed over several plots, with wild insects and sterile insects migrating between these plots. The main objective is to identify the critical plots for intervention, using the network connectivity and potential intervention constraints. Using results from monotone systems theory, we first derive a sufficient condition guaranteeing the elimination of the wild population through SIT, which relies on the sign of the Perron value of a certain Metzler matrix. When an Allee effect is naturally present, releases are finite in time, and an upper bound of the control time is provided. We then formulate an optimisation problem aimed at minimising the total daily number of sterile insects released to ensure population elimination. We focus in particular on the oriental fruit fly, which significantly impacts mango orchards in La R\'eunion. Through numerical simulations, we illustrate our theoretical results and study different scenarios, including some where releases are limited to certain orchards. Indeed, when implementing SIT in the field, some owners may be reluctant to allow releases on their property. We also consider additional control by mass trapping, which can affect the sterile insects entering trapped areas, and show that although it increases the critical number of sterile insects to be released daily, it reduces the duration of the SIT program. Mass trapping may thus decrease the total number of sterile insects released over the entire elimination program.