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Predictability in a highly stochastic system: final size of measles epidemics in small populations

A standard assumption in the modelling of epidemic dynamics is that the population of interest is well mixed, and that no clusters of metapopulations exist. The well-known and oft-used SIR model, arguably the most important compartmental model in theoretical epidemiology, assumes that the disease be...

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Autores principales: Caudron, Q., Mahmud, A. S., Metcalf, C. J. E., Gottfreðsson, M., Viboud, C., Cliff, A. D., Grenfell, B. T.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society 2015
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4277111/
https://www.ncbi.nlm.nih.gov/pubmed/25411411
http://dx.doi.org/10.1098/rsif.2014.1125
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author Caudron, Q.
Mahmud, A. S.
Metcalf, C. J. E.
Gottfreðsson, M.
Viboud, C.
Cliff, A. D.
Grenfell, B. T.
author_facet Caudron, Q.
Mahmud, A. S.
Metcalf, C. J. E.
Gottfreðsson, M.
Viboud, C.
Cliff, A. D.
Grenfell, B. T.
author_sort Caudron, Q.
collection PubMed
description A standard assumption in the modelling of epidemic dynamics is that the population of interest is well mixed, and that no clusters of metapopulations exist. The well-known and oft-used SIR model, arguably the most important compartmental model in theoretical epidemiology, assumes that the disease being modelled is strongly immunizing, directly transmitted and has a well-defined period of infection, in addition to these population mixing assumptions. Childhood infections, such as measles, are prime examples of diseases that fit the SIR-like mechanism. These infections have been well studied for many systems with large, well-mixed populations with endemic infection. Here, we consider a setting where populations are small and isolated. The dynamics of infection are driven by stochastic extinction–recolonization events, producing large, sudden and short-lived epidemics before rapidly dying out from a lack of susceptible hosts. Using a TSIR model, we fit prevaccination measles incidence and demographic data in Bornholm, the Faroe Islands and four districts of Iceland, between 1901 and 1965. The datasets for each of these countries suffer from different levels of data heterogeneity and sparsity. We explore the potential for prediction of this model: given historical incidence data and up-to-date demographic information, and knowing that a new epidemic has just begun, can we predict how large it will be? We show that, despite a lack of significant seasonality in the incidence of measles cases, and potentially severe heterogeneity at the population level, we are able to estimate the size of upcoming epidemics, conditioned on the first time step, to within reasonable confidence. Our results have potential implications for possible control measures for the early stages of new epidemics in small populations.
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spelling pubmed-42771112015-01-06 Predictability in a highly stochastic system: final size of measles epidemics in small populations Caudron, Q. Mahmud, A. S. Metcalf, C. J. E. Gottfreðsson, M. Viboud, C. Cliff, A. D. Grenfell, B. T. J R Soc Interface Research Articles A standard assumption in the modelling of epidemic dynamics is that the population of interest is well mixed, and that no clusters of metapopulations exist. The well-known and oft-used SIR model, arguably the most important compartmental model in theoretical epidemiology, assumes that the disease being modelled is strongly immunizing, directly transmitted and has a well-defined period of infection, in addition to these population mixing assumptions. Childhood infections, such as measles, are prime examples of diseases that fit the SIR-like mechanism. These infections have been well studied for many systems with large, well-mixed populations with endemic infection. Here, we consider a setting where populations are small and isolated. The dynamics of infection are driven by stochastic extinction–recolonization events, producing large, sudden and short-lived epidemics before rapidly dying out from a lack of susceptible hosts. Using a TSIR model, we fit prevaccination measles incidence and demographic data in Bornholm, the Faroe Islands and four districts of Iceland, between 1901 and 1965. The datasets for each of these countries suffer from different levels of data heterogeneity and sparsity. We explore the potential for prediction of this model: given historical incidence data and up-to-date demographic information, and knowing that a new epidemic has just begun, can we predict how large it will be? We show that, despite a lack of significant seasonality in the incidence of measles cases, and potentially severe heterogeneity at the population level, we are able to estimate the size of upcoming epidemics, conditioned on the first time step, to within reasonable confidence. Our results have potential implications for possible control measures for the early stages of new epidemics in small populations. The Royal Society 2015-01-06 /pmc/articles/PMC4277111/ /pubmed/25411411 http://dx.doi.org/10.1098/rsif.2014.1125 Text en http://creativecommons.org/licenses/by/4.0/ © 2014 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
spellingShingle Research Articles
Caudron, Q.
Mahmud, A. S.
Metcalf, C. J. E.
Gottfreðsson, M.
Viboud, C.
Cliff, A. D.
Grenfell, B. T.
Predictability in a highly stochastic system: final size of measles epidemics in small populations
title Predictability in a highly stochastic system: final size of measles epidemics in small populations
title_full Predictability in a highly stochastic system: final size of measles epidemics in small populations
title_fullStr Predictability in a highly stochastic system: final size of measles epidemics in small populations
title_full_unstemmed Predictability in a highly stochastic system: final size of measles epidemics in small populations
title_short Predictability in a highly stochastic system: final size of measles epidemics in small populations
title_sort predictability in a highly stochastic system: final size of measles epidemics in small populations
topic Research Articles
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4277111/
https://www.ncbi.nlm.nih.gov/pubmed/25411411
http://dx.doi.org/10.1098/rsif.2014.1125
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