The effects of heterogeneity on stochastic cycles in epidemics

Abstract 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, whic...

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Autores principales:	Francisco Herrerías-Azcué, Tobias Galla
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/0d44a3bdbe7d44fd981d7c2a93ab0384
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spelling	oai:doaj.org-article:0d44a3bdbe7d44fd981d7c2a93ab03842021-12-02T15:04:53ZThe effects of heterogeneity on stochastic cycles in epidemics10.1038/s41598-017-12606-x2045-2322https://doaj.org/article/0d44a3bdbe7d44fd981d7c2a93ab03842017-10-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-12606-xhttps://doaj.org/toc/2045-2322Abstract 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.Francisco Herrerías-AzcuéTobias GallaNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-14 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Francisco Herrerías-Azcué Tobias Galla The effects of heterogeneity on stochastic cycles in epidemics
description	Abstract 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.
format	article
author	Francisco Herrerías-Azcué Tobias Galla
author_facet	Francisco Herrerías-Azcué Tobias Galla
author_sort	Francisco Herrerías-Azcué
title	The effects of heterogeneity on stochastic cycles in epidemics
title_short	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_sort	effects of heterogeneity on stochastic cycles in epidemics
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/0d44a3bdbe7d44fd981d7c2a93ab0384
work_keys_str_mv	AT franciscoherreriasazcue theeffectsofheterogeneityonstochasticcyclesinepidemics AT tobiasgalla theeffectsofheterogeneityonstochasticcyclesinepidemics AT franciscoherreriasazcue effectsofheterogeneityonstochasticcyclesinepidemics AT tobiasgalla effectsofheterogeneityonstochasticcyclesinepidemics
_version_	1718388998857031680

The effects of heterogeneity on stochastic cycles in epidemics

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