De Reggi, S., Scarabel, F. orcid.org/0000-0003-0250-4555 and Vermiglio, R. (2024) Approximating reproduction numbers: a general numerical method for age-structured models. Mathematical Biosciences and Engineering, 21 (4). pp. 5360-5393. ISSN 1547-1063
Abstract
In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility in the definition of the birth and transition processes, we propose an equivalent formulation for the age-integrated state within the extended space framework. Then, we discretize the birth and transition operators via pseudospectral collocation. We discuss applications to epidemic models with continuous and piecewise continuous rates, with different interpretations of the age variable (e.g., demographic age, infection age and disease age) and the transmission terms (e.g., horizontal and vertical transmission). The tests illustrate that the method can compute different reproduction numbers, including the basic and type reproduction numbers as special cases.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 the Author(s), licensee AIMS Press. This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | basic reproduction number; structured population dynamics; epidemic models; next generation operator; pseudospectral collocation; eigenvalue approximation |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 15 Mar 2024 11:06 |
Last Modified: | 15 Mar 2024 11:06 |
Status: | Published |
Publisher: | AIMS Press |
Identification Number: | 10.3934/mbe.2024236 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:210267 |