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    Rights statement: This is the author’s version of a work that was accepted for publication in Mathematical Biosciences. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Mathematical Biosciences, 315, 2019 DOI: 10.1016/j.mbs.2019.108224

    Accepted author manuscript, 383 KB, PDF document

    Embargo ends: 2/07/20

    Available under license: CC BY-NC-ND

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The basic reproduction number, R_0, in structured populations

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Article number108224
<mark>Journal publication date</mark>1/09/2019
<mark>Journal</mark>Mathematical Biosciences
Volume315
Number of pages12
Publication statusPublished
Early online date2/07/19
Original languageEnglish

Abstract

In this paper, we provide a straightforward approach to defining and deriving the key epidemiological quantity, the basic reproduction number, $R_0$, for Markovian epidemics in structured populations. The methodology derived is applicable to, and demonstrated on, both $SIR$ and $SIS$ epidemics and allows for population as well as epidemic dynamics. The approach taken is to consider the epidemic process as a multitype process by identifying and classifying the different types of infectious units along with the infections from, and the transitions between, infectious units. For the household model, we show that our expression for $R_0$ agrees with earlier work despite the alternative nature of the construction of the mean reproductive matrix, and hence, the basic reproduction number.

Bibliographic note

This is the author’s version of a work that was accepted for publication in Mathematical Biosciences. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Mathematical Biosciences, 315, 2019 DOI: 10.1016/j.mbs.2019.108224