Résumé
This work explores optimal strategies for the elimination of a fly population through adult mass trapping and larval treatment.Building on the results of [1] for (single-stage) metapopulation models with logistic growth, we extend here the analysis to a structured model that distinguishes between larvae, females and males. Linear migration of adults between patches is included, and the dynamic in each patch is inspired by the model in [2,3].Under appropriate conditions, we derive a condition that guarantees either elimination in all patches or convergence to a unique positive equilibrium.Then, additional larval and adult mortality terms are introduced in a subset of `controllable' patches, where intervention is allowed.We show that the feasibility of population elimination is determined by an algebraic property on the Jacobian at the origin of a so-called residual system. When elimination is feasible, the successful strategies that minimise a suitable treatment effort are analysed and compared with those established for the simpler logistic model considered in [1].