Résumé
The sterile insect technique (SIT) is a biological control method aimed at reduc-ing or eliminating populations of pests or disease vectors. This technique involvesreleasing sterilised insects which, by mating with wild individuals, reduce the targetpopulation [1]. In this study, we incorporate spatial structure by modelling the pop-ulation as distributed across interconnected plots, through a metapopulation model.We focus in particular on the oriental fruit fly, which significantly impacts mangoorchards in La R´eunion.Using results from monotone cooperative systems [3], we derive a su!cient con-dition for the elimination of the wild population through SIT, which relies on thesign of the Perron value of a certain Metlzer matrix. In the presence of a strongnatural Allee e”ect, releases can be finite in time, and we provide an estimate of therequired treatment duration. We then formulate an optimisation problem aimed atminimising the total daily number of sterile insects released to ensure populationelimination. By exploiting the convexity properties of the Perron value of a Metzlermatrix with respect to its diagonal entries [2], this problem is shown to be convex.Through numerical simulations, we illustrate the obtained theoretical resultsand study di”erent scenarios, including some where releases are limited to certainorchards. Indeed, when implementing SIT in the field, some owners may be reluctantto allow releases on their property. We also consider additional control by masstrapping, which can a”ect as well the sterile insects entering trapped areas. Evenif this operation requires an increase in the sterile insect release rate, it reducesthe duration of the SIT campaign, and therefore may decrease the total number ofsterile insects released over the entire program.