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
Available under license: CC BY-NC-ND
Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - The basic reproduction number, R_0, in structured populations
AU - Neal, Peter
AU - Theparod, Thitiya
N1 - 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
PY - 2019/9/1
Y1 - 2019/9/1
N2 - 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.
AB - 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.
U2 - 10.1016/j.mbs.2019.108224
DO - 10.1016/j.mbs.2019.108224
M3 - Journal article
VL - 315
JO - Mathematical Biosciences
JF - Mathematical Biosciences
SN - 0025-5564
M1 - 108224
ER -