Hamiltonian dynamics of the SIS epidemic model with stochastic fluctuations

Abstract Empirical records of epidemics reveal that fluctuations are important factors for the spread and prevalence of infectious diseases. The exact manner in which fluctuations affect spreading dynamics remains poorly known. Recent analytical and numerical studies have demonstrated that improved...

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Autores principales:	Gilberto M. Nakamura, Alexandre S. Martinez
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2019
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/35dca6943c384defa2992a7a4864cfde
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spelling	oai:doaj.org-article:35dca6943c384defa2992a7a4864cfde2021-12-02T15:09:15ZHamiltonian dynamics of the SIS epidemic model with stochastic fluctuations10.1038/s41598-019-52351-x2045-2322https://doaj.org/article/35dca6943c384defa2992a7a4864cfde2019-11-01T00:00:00Zhttps://doi.org/10.1038/s41598-019-52351-xhttps://doaj.org/toc/2045-2322Abstract Empirical records of epidemics reveal that fluctuations are important factors for the spread and prevalence of infectious diseases. The exact manner in which fluctuations affect spreading dynamics remains poorly known. Recent analytical and numerical studies have demonstrated that improved differential equations for mean and variance of infected individuals reproduce certain regimes of the SIS epidemic model. Here, we show they form a dynamical system that follows Hamilton’s equations, which allow us to understand the role of fluctuations and their effects on epidemics. Our findings show the Hamiltonian is a constant of motion for large population sizes. For small populations, finite size effects break the temporal symmetry and induce a power-law decay of the Hamiltonian near the outbreak onset, with a parameter-free exponent. Away from the onset, the Hamiltonian decays exponentially according to a constant relaxation time, which we propose as a metric when fluctuations cannot be neglected.Gilberto M. NakamuraAlexandre S. MartinezNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 9, Iss 1, Pp 1-9 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Gilberto M. Nakamura Alexandre S. Martinez Hamiltonian dynamics of the SIS epidemic model with stochastic fluctuations
description	Abstract Empirical records of epidemics reveal that fluctuations are important factors for the spread and prevalence of infectious diseases. The exact manner in which fluctuations affect spreading dynamics remains poorly known. Recent analytical and numerical studies have demonstrated that improved differential equations for mean and variance of infected individuals reproduce certain regimes of the SIS epidemic model. Here, we show they form a dynamical system that follows Hamilton’s equations, which allow us to understand the role of fluctuations and their effects on epidemics. Our findings show the Hamiltonian is a constant of motion for large population sizes. For small populations, finite size effects break the temporal symmetry and induce a power-law decay of the Hamiltonian near the outbreak onset, with a parameter-free exponent. Away from the onset, the Hamiltonian decays exponentially according to a constant relaxation time, which we propose as a metric when fluctuations cannot be neglected.
format	article
author	Gilberto M. Nakamura Alexandre S. Martinez
author_facet	Gilberto M. Nakamura Alexandre S. Martinez
author_sort	Gilberto M. Nakamura
title	Hamiltonian dynamics of the SIS epidemic model with stochastic fluctuations
title_short	Hamiltonian dynamics of the SIS epidemic model with stochastic fluctuations
title_full	Hamiltonian dynamics of the SIS epidemic model with stochastic fluctuations
title_fullStr	Hamiltonian dynamics of the SIS epidemic model with stochastic fluctuations
title_full_unstemmed	Hamiltonian dynamics of the SIS epidemic model with stochastic fluctuations
title_sort	hamiltonian dynamics of the sis epidemic model with stochastic fluctuations
publisher	Nature Portfolio
publishDate	2019
url	https://doaj.org/article/35dca6943c384defa2992a7a4864cfde
work_keys_str_mv	AT gilbertomnakamura hamiltoniandynamicsofthesisepidemicmodelwithstochasticfluctuations AT alexandresmartinez hamiltoniandynamicsofthesisepidemicmodelwithstochasticfluctuations
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Hamiltonian dynamics of the SIS epidemic model with stochastic fluctuations

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