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The effects of heterogeneity on stochastic cycles in epidemics

Models of biological processes are often subject to different sources of noise. Developing an understanding of the combined effects of different types of uncertainty is an open challenge. In this paper, we study a variant of the susceptible-infective-recovered model of epidemic spread, which combine...

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Autores principales: Herrerías-Azcué, Francisco, Galla, Tobias
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5636822/
https://www.ncbi.nlm.nih.gov/pubmed/29021550
http://dx.doi.org/10.1038/s41598-017-12606-x
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author Herrerías-Azcué, Francisco
Galla, Tobias
author_facet Herrerías-Azcué, Francisco
Galla, Tobias
author_sort Herrerías-Azcué, Francisco
collection PubMed
description Models of biological processes are often subject to different sources of noise. Developing an understanding of the combined effects of different types of uncertainty is an open challenge. In this paper, we study a variant of the susceptible-infective-recovered model of epidemic spread, which combines both agent-to-agent heterogeneity and intrinsic noise. We focus on epidemic cycles, driven by the stochasticity of infection and recovery events, and study in detail how heterogeneity in susceptibilities and propensities to pass on the disease affects these quasi-cycles. While the system can only be described by a large hierarchical set of equations in the transient regime, we derive a reduced closed set of equations for population-level quantities in the stationary regime. We analytically obtain the spectra of quasi-cycles in the linear-noise approximation. We find that the characteristic frequency of these cycles is typically determined by population averages of susceptibilities and infectivities, but that their amplitude depends on higher-order moments of the heterogeneity. We also investigate the synchronisation properties and phase lag between different groups of susceptible and infected individuals.
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spelling pubmed-56368222017-10-18 The effects of heterogeneity on stochastic cycles in epidemics Herrerías-Azcué, Francisco Galla, Tobias Sci Rep Article Models of biological processes are often subject to different sources of noise. Developing an understanding of the combined effects of different types of uncertainty is an open challenge. In this paper, we study a variant of the susceptible-infective-recovered model of epidemic spread, which combines both agent-to-agent heterogeneity and intrinsic noise. We focus on epidemic cycles, driven by the stochasticity of infection and recovery events, and study in detail how heterogeneity in susceptibilities and propensities to pass on the disease affects these quasi-cycles. While the system can only be described by a large hierarchical set of equations in the transient regime, we derive a reduced closed set of equations for population-level quantities in the stationary regime. We analytically obtain the spectra of quasi-cycles in the linear-noise approximation. We find that the characteristic frequency of these cycles is typically determined by population averages of susceptibilities and infectivities, but that their amplitude depends on higher-order moments of the heterogeneity. We also investigate the synchronisation properties and phase lag between different groups of susceptible and infected individuals. Nature Publishing Group UK 2017-10-11 /pmc/articles/PMC5636822/ /pubmed/29021550 http://dx.doi.org/10.1038/s41598-017-12606-x Text en © The Author(s) 2017 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Herrerías-Azcué, Francisco
Galla, Tobias
The effects of heterogeneity on stochastic cycles in epidemics
title The effects of heterogeneity on stochastic cycles in epidemics
title_full The effects of heterogeneity on stochastic cycles in epidemics
title_fullStr The effects of heterogeneity on stochastic cycles in epidemics
title_full_unstemmed The effects of heterogeneity on stochastic cycles in epidemics
title_short The effects of heterogeneity on stochastic cycles in epidemics
title_sort effects of heterogeneity on stochastic cycles in epidemics
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5636822/
https://www.ncbi.nlm.nih.gov/pubmed/29021550
http://dx.doi.org/10.1038/s41598-017-12606-x
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