On the basic reproduction number in continuously structured populations
Barril, Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Calsina i Ballesta, Àngel (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Cuadrado Gavilán, Sílvia (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Ripoll, Jordi (Universitat de Girona. Departament d'Informàtica, Matemàtica Aplicada i Estadística)

Date:	2021
Abstract:	In the framework of population dynamics, the basic reproduction number (Formula presented. ) is, by definition, the expected number of offspring that an individual has during its lifetime. In constant and time periodic environments, it is calculated as the spectral radius of the so-called next-generation operator. In continuously structured populations defined in a Banach lattice X with concentrated states at birth, one cannot define the next-generation operator in X. In the present paper, we present an approach to compute the basic reproduction number of such models as the limit of the basic reproduction number of a sequence of models for which (Formula presented. ) can be computed as the spectral radius of the next-generation operator. We apply these results to some examples: the (classical) size-dependent model, a size-structured cell population model, a size-structured model with diffusion in structure space (under some particular assumptions), and a (physiological) age-structured model with diffusion in structure space.
Grants:	Agencia Estatal de Investigación MTM2017-84214-C2-2-P Ministerio de Ciencia e Innovación RED2018-102650-T
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Basic reproduction number ; Next-generation operator ; Physiologically structured population
Published in:	Mathematical methods in the applied sciences, Vol. 44, Issue 1 (January 2021) , p. 799-812, ISSN 1099-1476

DOI: 10.1002/mma.6787

Postprint 19 p, 512.9 KB

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