Feasibility and optimisation of fly elimination by adult mass trapping and larval treatment : a stage-structured metapopulation approach

Abstract

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].

References

[1] P-A. Bliman, M. de la Tousche, Y. Dumont, Feasibility and optimisation results for elimination by mass trapping in a metapopulation model, Appl. Math. Model., 144:116047, 2025.

[2] M. Strugarek, H. Bossin, Y. Dumont, On the use of the sterile insect release technique to
reduce or eliminate mosquito populations, Appl. Math. Model., 68:443-470, 2019.

[3] R. Anguelov, Y. Dumont, I.V. Yatat Djeumen, Sustainable vector/pest control using the
permanent sterile insect technique, Math. Meth. Appl. Sci., 43:10391{10412, 2020.