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

Pierre-Alexandre Bliman, Manon de la Tousche, Yves Dumont

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Pierre-Alexandre Bliman, Manon de la Tousche, Yves Dumont. Feasibility and optimisation of fly elimination by adult mass trapping and larval treatment: a stage-structured metapopulation approach. BIOMATH2025 - International Conference on Mathematical Methods and Models in Biosciences, Jun 2025, Sofia, Bulgaria. hal-05114647

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Submitted on 16 Jun 2025

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Distributed under a Creative Commons Attribution 4.0 International License
Mathematical Methods and Models in Biosciences

June 15–20, 2025, Sofia, Bulgaria

https://biomath.math.bas.bg/biomath/index.php/bmcs

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

Pierre-Alexandre Bliman<fnref n="1" />, Manon de la Tousche<fnref n="1" />,<fnref n="3" />, Yves Dumont<fnref n="2" />,<fnref n="3" />,<fnref n="4" />

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.

<footnote n="1">¹Sorbonne Université, Université Paris Cité, CNRS, Inria, Laboratoire Jacques-Louis Lions, LJLL, EPC MUSCLEES, F-75005 Paris, France
pierre-alexandre.bliman@inria.fr, manon.de-la-tousche@inria.fr</footnote>

<footnote n="2">²CIRAD, UMR AMAP, Pôle de Protection des Plantes, F-97410 Saint Pierre, France,
yves.dumont@cirad.fr</footnote>

<footnote n="3">³AMAP, Univ Montpellier, CIRAD, CNRS, INRA, IRD, Montpellier, France</footnote>

<footnote n="4">⁴University of Pretoria, Department of Mathematics and Applied Mathematics, Pretoria, South Africa</footnote>
[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.