Pré-Publication, Document De Travail Année : 2025

Remarks on invasion threshold for structured population models

Résumé

We develop a unified framework for computing threshold quantities-serving as analogues to the basic reproduction number R 0 -in a broad class of structured population models formulated in infinite-dimensional Banach spaces. While classical approaches allow for an explicit derivation of threshold operators in finite-dimensional settings, such systematic methodologies are lacking in infinite-dimensional contexts. This work addresses that gap by proposing a direct, step-by-step construction of a threshold operator that captures the long-term dynamics of the system. The framework accommodates models governed by hyperbolic, parabolic, and delay differential equations, thereby covering a wide range of applications in population dynamics. We illustrate the methodology through several examples, including both epidemiological and ecological models with age, spatial, or physiological structure.

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hal-05142856 , version 1 (03-07-2025)

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  • HAL Id : hal-05142856 , version 1

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Ramsès Djidjou-Demasse, Arnaud Ducrot, Malick Pane, Ousmane Seydi. Remarks on invasion threshold for structured population models. 2025. ⟨hal-05142856⟩
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