An agile modeling framework for population dynamics

• Published in: Mathematics and computers in simulation Vol. 234; pp. 113 - 134
• Main Authors: Attias, Laurent, Siess, Vincent, Labbé, Stéphane
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.2025
• Subjects: Bifurcations; McKendrick equation; Model generation; Population dynamics; Predator–prey model; Structured population models; McKendrick equation; 92D30; 35Q49; 92D25; Model generation; 92-10; Bifurcations; Population dynamics; 65P30; Predator–prey model; 34K20; Structured population models
• ISSN: 0378-4754
• DOI: 10.1016/j.matcom.2025.02.013

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.