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The stochastic dynamics of early epidemics: probability of establishment, initial growth rate, and infection cluster size at first detection

Emerging epidemics and local infection clusters are initially prone to stochastic effects that can substantially impact the early epidemic trajectory. While numerous studies are devoted to the deterministic regime of an established epidemic, mathematical descriptions of the initial phase of epidemic...

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Autores principales: Czuppon, Peter, Schertzer, Emmanuel, Blanquart, François, Débarre, Florence
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8596012/
https://www.ncbi.nlm.nih.gov/pubmed/34784776
http://dx.doi.org/10.1098/rsif.2021.0575
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author Czuppon, Peter
Schertzer, Emmanuel
Blanquart, François
Débarre, Florence
author_facet Czuppon, Peter
Schertzer, Emmanuel
Blanquart, François
Débarre, Florence
author_sort Czuppon, Peter
collection PubMed
description Emerging epidemics and local infection clusters are initially prone to stochastic effects that can substantially impact the early epidemic trajectory. While numerous studies are devoted to the deterministic regime of an established epidemic, mathematical descriptions of the initial phase of epidemic growth are comparatively rarer. Here, we review existing mathematical results on the size of the epidemic over time, and derive new results to elucidate the early dynamics of an infection cluster started by a single infected individual. We show that the initial growth of epidemics that eventually take off is accelerated by stochasticity. As an application, we compute the distribution of the first detection time of an infected individual in an infection cluster depending on testing effort, and estimate that the SARS-CoV-2 variant of concern Alpha detected in September 2020 first appeared in the UK early August 2020. We also compute a minimal testing frequency to detect clusters before they exceed a given threshold size. These results improve our theoretical understanding of early epidemics and will be useful for the study and control of local infectious disease clusters.
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spelling pubmed-85960122021-11-17 The stochastic dynamics of early epidemics: probability of establishment, initial growth rate, and infection cluster size at first detection Czuppon, Peter Schertzer, Emmanuel Blanquart, François Débarre, Florence J R Soc Interface Life Sciences–Mathematics interface Emerging epidemics and local infection clusters are initially prone to stochastic effects that can substantially impact the early epidemic trajectory. While numerous studies are devoted to the deterministic regime of an established epidemic, mathematical descriptions of the initial phase of epidemic growth are comparatively rarer. Here, we review existing mathematical results on the size of the epidemic over time, and derive new results to elucidate the early dynamics of an infection cluster started by a single infected individual. We show that the initial growth of epidemics that eventually take off is accelerated by stochasticity. As an application, we compute the distribution of the first detection time of an infected individual in an infection cluster depending on testing effort, and estimate that the SARS-CoV-2 variant of concern Alpha detected in September 2020 first appeared in the UK early August 2020. We also compute a minimal testing frequency to detect clusters before they exceed a given threshold size. These results improve our theoretical understanding of early epidemics and will be useful for the study and control of local infectious disease clusters. The Royal Society 2021-11-17 /pmc/articles/PMC8596012/ /pubmed/34784776 http://dx.doi.org/10.1098/rsif.2021.0575 Text en © 2021 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
Czuppon, Peter
Schertzer, Emmanuel
Blanquart, François
Débarre, Florence
The stochastic dynamics of early epidemics: probability of establishment, initial growth rate, and infection cluster size at first detection
title The stochastic dynamics of early epidemics: probability of establishment, initial growth rate, and infection cluster size at first detection
title_full The stochastic dynamics of early epidemics: probability of establishment, initial growth rate, and infection cluster size at first detection
title_fullStr The stochastic dynamics of early epidemics: probability of establishment, initial growth rate, and infection cluster size at first detection
title_full_unstemmed The stochastic dynamics of early epidemics: probability of establishment, initial growth rate, and infection cluster size at first detection
title_short The stochastic dynamics of early epidemics: probability of establishment, initial growth rate, and infection cluster size at first detection
title_sort stochastic dynamics of early epidemics: probability of establishment, initial growth rate, and infection cluster size at first detection
topic Life Sciences–Mathematics interface
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8596012/
https://www.ncbi.nlm.nih.gov/pubmed/34784776
http://dx.doi.org/10.1098/rsif.2021.0575
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