On the basic reproduction number in continuously structured populations

[2002.10557] On the basic reproduction number in continuously structured populations Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Analysis of PDEs arXiv:2002.10557 (math) [Submitted on 24 Feb 2020] Title: On the basic reproduction number in continuously structured populations Authors: Carles Barril , Àngel Calsina , Sílvia Cuadrado , Jordi Ripoll View a PDF of the paper titled On the basic reproduction number in continuously structured populations, by Carles Barril and 2 other authors View PDF HTML (experimental) Abstract: In the framework of population dynamics, the basic reproduction number R_0 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 R_0 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. Subjects: Analysis of PDEs (math.AP) ; Populations and Evolution (q-bio.PE) MSC classes: 92D25, 35Q92 Cite as: arXiv:2002.10557 [math.AP] (or arXiv:2002.10557v1 [math.AP] for this version) https://doi.org/10.48550/arXiv.2002.10557 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Math Meth Appl Sci. 2021;44:799-812 Related DOI : https://doi.org/10.1002/mma.6787 Focus to learn more DOI(s) linking to related resources Submission history From: Jordi Ripoll [ view email ] [v1] Mon, 24 Feb 2020 21:51:26 UTC (31 KB) Full-text links: Access Paper: View a PDF of the paper titled On the basic reproduction number in continuously structured populations, by Carles Barril and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2020-02 Change to browse by: math q-bio q-bio.PE References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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