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Inferring the reproduction number using the renewal equation in heterogeneous epidemics

Real-time estimation of the reproduction number has become the focus of modelling groups around the world as the SARS-CoV-2 pandemic unfolds. One of the most widely adopted means of inference of the reproduction number is via the renewal equation, which uses the incidence of infection and the genera...

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Detalles Bibliográficos
Autores principales: Green, William D., Ferguson, Neil M., Cori, Anne
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8965414/
https://www.ncbi.nlm.nih.gov/pubmed/35350879
http://dx.doi.org/10.1098/rsif.2021.0429
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author Green, William D.
Ferguson, Neil M.
Cori, Anne
author_facet Green, William D.
Ferguson, Neil M.
Cori, Anne
author_sort Green, William D.
collection PubMed
description Real-time estimation of the reproduction number has become the focus of modelling groups around the world as the SARS-CoV-2 pandemic unfolds. One of the most widely adopted means of inference of the reproduction number is via the renewal equation, which uses the incidence of infection and the generation time distribution. In this paper, we derive a multi-type equivalent to the renewal equation to estimate a reproduction number which accounts for heterogeneity in transmissibility including through asymptomatic transmission, symptomatic isolation and vaccination. We demonstrate how use of the renewal equation that misses these heterogeneities can result in biased estimates of the reproduction number. While the bias is small with symptomatic isolation, it can be much larger with asymptomatic transmission or transmission from vaccinated individuals if these groups exhibit substantially different generation time distributions to unvaccinated symptomatic transmitters, whose generation time distribution is often well defined. The bias in estimate becomes larger with greater population size or transmissibility of the poorly characterized group. We apply our methodology to Ebola in West Africa in 2014 and the SARS-CoV-2 in the UK in 2020–2021.
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spelling pubmed-89654142022-03-30 Inferring the reproduction number using the renewal equation in heterogeneous epidemics Green, William D. Ferguson, Neil M. Cori, Anne J R Soc Interface Life Sciences–Mathematics interface Real-time estimation of the reproduction number has become the focus of modelling groups around the world as the SARS-CoV-2 pandemic unfolds. One of the most widely adopted means of inference of the reproduction number is via the renewal equation, which uses the incidence of infection and the generation time distribution. In this paper, we derive a multi-type equivalent to the renewal equation to estimate a reproduction number which accounts for heterogeneity in transmissibility including through asymptomatic transmission, symptomatic isolation and vaccination. We demonstrate how use of the renewal equation that misses these heterogeneities can result in biased estimates of the reproduction number. While the bias is small with symptomatic isolation, it can be much larger with asymptomatic transmission or transmission from vaccinated individuals if these groups exhibit substantially different generation time distributions to unvaccinated symptomatic transmitters, whose generation time distribution is often well defined. The bias in estimate becomes larger with greater population size or transmissibility of the poorly characterized group. We apply our methodology to Ebola in West Africa in 2014 and the SARS-CoV-2 in the UK in 2020–2021. The Royal Society 2022-03-30 /pmc/articles/PMC8965414/ /pubmed/35350879 http://dx.doi.org/10.1098/rsif.2021.0429 Text en © 2022 The Authors. https://creativecommons.org/licenses/by/4.0/Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, provided the original author and source are credited.
spellingShingle Life Sciences–Mathematics interface
Green, William D.
Ferguson, Neil M.
Cori, Anne
Inferring the reproduction number using the renewal equation in heterogeneous epidemics
title Inferring the reproduction number using the renewal equation in heterogeneous epidemics
title_full Inferring the reproduction number using the renewal equation in heterogeneous epidemics
title_fullStr Inferring the reproduction number using the renewal equation in heterogeneous epidemics
title_full_unstemmed Inferring the reproduction number using the renewal equation in heterogeneous epidemics
title_short Inferring the reproduction number using the renewal equation in heterogeneous epidemics
title_sort inferring the reproduction number using the renewal equation in heterogeneous epidemics
topic Life Sciences–Mathematics interface
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8965414/
https://www.ncbi.nlm.nih.gov/pubmed/35350879
http://dx.doi.org/10.1098/rsif.2021.0429
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