Cargando…
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...
Autores principales: | , , , |
---|---|
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 |
_version_ | 1784600270080049152 |
---|---|
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. |
format | Online Article Text |
id | pubmed-8596012 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | The Royal Society |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT czupponpeter thestochasticdynamicsofearlyepidemicsprobabilityofestablishmentinitialgrowthrateandinfectionclustersizeatfirstdetection AT schertzeremmanuel thestochasticdynamicsofearlyepidemicsprobabilityofestablishmentinitialgrowthrateandinfectionclustersizeatfirstdetection AT blanquartfrancois thestochasticdynamicsofearlyepidemicsprobabilityofestablishmentinitialgrowthrateandinfectionclustersizeatfirstdetection AT debarreflorence thestochasticdynamicsofearlyepidemicsprobabilityofestablishmentinitialgrowthrateandinfectionclustersizeatfirstdetection AT czupponpeter stochasticdynamicsofearlyepidemicsprobabilityofestablishmentinitialgrowthrateandinfectionclustersizeatfirstdetection AT schertzeremmanuel stochasticdynamicsofearlyepidemicsprobabilityofestablishmentinitialgrowthrateandinfectionclustersizeatfirstdetection AT blanquartfrancois stochasticdynamicsofearlyepidemicsprobabilityofestablishmentinitialgrowthrateandinfectionclustersizeatfirstdetection AT debarreflorence stochasticdynamicsofearlyepidemicsprobabilityofestablishmentinitialgrowthrateandinfectionclustersizeatfirstdetection |