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An agile modeling framework for population dynamics

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  • Attias, Laurent
  • Siess, Vincent
  • Labbé, Stéphane

Abstract

In this work, we present an agile modeling framework for structured population dynamics, leading to automated generation of population models’ equations. The structure of a population, i.e. its separation in strata, according to one or many criteria (such as sex, income, health, geographic area or species if dealing with animal populations), represents a major issue for the precision and richness of population dynamics simulations. The intensity of some phenomena and mechanisms is highly dependent on the involved subpopulation characteristics. This modeling framework can be seen as an extension of the classic McKendrick–von Foerster equation, which embeds the population structure. It allows showing, under appropriate hypothesis, an existence and local uniqueness result for the solution of a transport equation. A modeler has been implemented, to generate models that respect the desired structure hypotheses. We illustrate its abilities on an age-structured predator–prey model, subject to migratory dynamics and to an epidemic, based on a SIRD model.

Suggested Citation

  • Attias, Laurent & Siess, Vincent & Labbé, Stéphane, 2025. "An agile modeling framework for population dynamics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 234(C), pages 113-134.
    • Handle: RePEc:eee:matcom:v:234:y:2025:i:c:p:113-134
    DOI: 10.1016/j.matcom.2025.02.013
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    References listed on IDEAS

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    1. Uyenoyama, Marcy K. & Takebayashi, Naoki & Kumagai, Seiji, 2019. "Inductive determination of allele frequency spectrum probabilities in structured populations," Theoretical Population Biology, Elsevier, vol. 129(C), pages 148-159.
    2. Lu, Yang & Pawelek, Kasia A. & Liu, Shengqiang, 2017. "A stage-structured predator-prey model with predation over juvenile prey," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 115-130.
    3. Kumagai, Seiji & Uyenoyama, Marcy K., 2015. "Genealogical histories in structured populations," Theoretical Population Biology, Elsevier, vol. 102(C), pages 3-15.
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