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Integrating stochasticity and network structure into an epidemic model

While the foundations of modern epidemiology are based upon deterministic models with homogeneous mixing, it is being increasingly realized that both spatial structure and stochasticity play major roles in shaping epidemic dynamics. The integration of these two confounding elements is generally asce...

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Detalles Bibliográficos
Autores principales: Dangerfield, C. E., Ross, J. V., Keeling, M. J.
Formato: Texto
Lenguaje:English
Publicado: The Royal Society 2009
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2586797/
https://www.ncbi.nlm.nih.gov/pubmed/18974032
http://dx.doi.org/10.1098/rsif.2008.0410
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author Dangerfield, C. E.
Ross, J. V.
Keeling, M. J.
author_facet Dangerfield, C. E.
Ross, J. V.
Keeling, M. J.
author_sort Dangerfield, C. E.
collection PubMed
description While the foundations of modern epidemiology are based upon deterministic models with homogeneous mixing, it is being increasingly realized that both spatial structure and stochasticity play major roles in shaping epidemic dynamics. The integration of these two confounding elements is generally ascertained through numerical simulation. Here, for the first time, we develop a more rigorous analytical understanding based on pairwise approximations to incorporate localized spatial structure and diffusion approximations to capture the impact of stochasticity. Our results allow us to quantify, analytically, the impact of network structure on the variability of an epidemic. Using the susceptible–infectious–susceptible framework for the infection dynamics, the pairwise stochastic model is compared with the stochastic homogeneous-mixing (mean-field) model—although to enable a fair comparison the homogeneous-mixing parameters are scaled to give agreement with the pairwise dynamics. At equilibrium, we show that the pairwise model always displays greater variation about the mean, although the differences are generally small unless the prevalence of infection is low. By contrast, during the early epidemic growth phase when the level of infection is increasing exponentially, the pairwise model generally shows less variation.
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spelling pubmed-25867972008-11-25 Integrating stochasticity and network structure into an epidemic model Dangerfield, C. E. Ross, J. V. Keeling, M. J. J R Soc Interface Research Articles While the foundations of modern epidemiology are based upon deterministic models with homogeneous mixing, it is being increasingly realized that both spatial structure and stochasticity play major roles in shaping epidemic dynamics. The integration of these two confounding elements is generally ascertained through numerical simulation. Here, for the first time, we develop a more rigorous analytical understanding based on pairwise approximations to incorporate localized spatial structure and diffusion approximations to capture the impact of stochasticity. Our results allow us to quantify, analytically, the impact of network structure on the variability of an epidemic. Using the susceptible–infectious–susceptible framework for the infection dynamics, the pairwise stochastic model is compared with the stochastic homogeneous-mixing (mean-field) model—although to enable a fair comparison the homogeneous-mixing parameters are scaled to give agreement with the pairwise dynamics. At equilibrium, we show that the pairwise model always displays greater variation about the mean, although the differences are generally small unless the prevalence of infection is low. By contrast, during the early epidemic growth phase when the level of infection is increasing exponentially, the pairwise model generally shows less variation. The Royal Society 2009-09-06 2008-10-30 /pmc/articles/PMC2586797/ /pubmed/18974032 http://dx.doi.org/10.1098/rsif.2008.0410 Text en © 2008 The Royal Society http://creativecommons.org/licenses/by/2.5/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Articles
Dangerfield, C. E.
Ross, J. V.
Keeling, M. J.
Integrating stochasticity and network structure into an epidemic model
title Integrating stochasticity and network structure into an epidemic model
title_full Integrating stochasticity and network structure into an epidemic model
title_fullStr Integrating stochasticity and network structure into an epidemic model
title_full_unstemmed Integrating stochasticity and network structure into an epidemic model
title_short Integrating stochasticity and network structure into an epidemic model
title_sort integrating stochasticity and network structure into an epidemic model
topic Research Articles
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2586797/
https://www.ncbi.nlm.nih.gov/pubmed/18974032
http://dx.doi.org/10.1098/rsif.2008.0410
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