The basic reproduction number, R_0, in structured populations

Neal, Peter and Theparod, Thitiya (2019) The basic reproduction number, R_0, in structured populations. Mathematical Biosciences, 315. ISSN 0025-5564

Text (R0_paper)
R0_paper.pdf - Accepted Version
Available under License Creative Commons Attribution Non-commercial No Derivatives.

Download (392kB)


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.

Item Type:
Journal Article
Journal or Publication Title:
Mathematical Biosciences
Additional Information:
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
Uncontrolled Keywords:
ID Code:
Deposited By:
Deposited On:
22 Jul 2019 10:00
Last Modified:
19 Sep 2020 05:58