A paradox of epidemics between the state and parameter spaces

Abstract It is recently revealed from amounts of real data of recurrent epidemics that there is a phenomenon of hysteresis loop in the state space. To understand it, an indirect investigation from the parameter space has been given to qualitatively explain its mechanism but a more convincing study t...

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Autores principales:	Hengcong Liu, Muhua Zheng, Zonghua Liu
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2018
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/a1584530b215410fbb759725c098982e
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spelling	oai:doaj.org-article:a1584530b215410fbb759725c098982e2021-12-02T15:08:07ZA paradox of epidemics between the state and parameter spaces10.1038/s41598-018-25931-62045-2322https://doaj.org/article/a1584530b215410fbb759725c098982e2018-05-01T00:00:00Zhttps://doi.org/10.1038/s41598-018-25931-6https://doaj.org/toc/2045-2322Abstract It is recently revealed from amounts of real data of recurrent epidemics that there is a phenomenon of hysteresis loop in the state space. To understand it, an indirect investigation from the parameter space has been given to qualitatively explain its mechanism but a more convincing study to quantitatively explain the phenomenon directly from the state space is still missing. We here study this phenomenon directly from the state space and find that there is a positive correlation between the size of outbreak and the size of hysteresis loop, implying that the hysteresis is a nature feature of epidemic outbreak in real case. Moreover, we surprisingly find a paradox on the dependence of the size of hysteresis loop on the two parameters of the infectious rate increment and the transient time, i.e. contradictory behaviors between the two spaces, when the evolutionary time of epidemics is long enough. That is, with the increase of the infectious rate increment, the size of hysteresis loop will decrease in the state space but increase in the parameter space. While with the increase of the transient time, the size of hysteresis loop will increase in the state space but decrease in the parameter space. Furthermore, we find that this paradox will disappear when the evolutionary time of epidemics is limited in a fixed period. Some theoretical analysis are presented to both the paradox and other numerical results.Hengcong LiuMuhua ZhengZonghua LiuNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 8, Iss 1, Pp 1-11 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Hengcong Liu Muhua Zheng Zonghua Liu A paradox of epidemics between the state and parameter spaces
description	Abstract It is recently revealed from amounts of real data of recurrent epidemics that there is a phenomenon of hysteresis loop in the state space. To understand it, an indirect investigation from the parameter space has been given to qualitatively explain its mechanism but a more convincing study to quantitatively explain the phenomenon directly from the state space is still missing. We here study this phenomenon directly from the state space and find that there is a positive correlation between the size of outbreak and the size of hysteresis loop, implying that the hysteresis is a nature feature of epidemic outbreak in real case. Moreover, we surprisingly find a paradox on the dependence of the size of hysteresis loop on the two parameters of the infectious rate increment and the transient time, i.e. contradictory behaviors between the two spaces, when the evolutionary time of epidemics is long enough. That is, with the increase of the infectious rate increment, the size of hysteresis loop will decrease in the state space but increase in the parameter space. While with the increase of the transient time, the size of hysteresis loop will increase in the state space but decrease in the parameter space. Furthermore, we find that this paradox will disappear when the evolutionary time of epidemics is limited in a fixed period. Some theoretical analysis are presented to both the paradox and other numerical results.
format	article
author	Hengcong Liu Muhua Zheng Zonghua Liu
author_facet	Hengcong Liu Muhua Zheng Zonghua Liu
author_sort	Hengcong Liu
title	A paradox of epidemics between the state and parameter spaces
title_short	A paradox of epidemics between the state and parameter spaces
title_full	A paradox of epidemics between the state and parameter spaces
title_fullStr	A paradox of epidemics between the state and parameter spaces
title_full_unstemmed	A paradox of epidemics between the state and parameter spaces
title_sort	paradox of epidemics between the state and parameter spaces
publisher	Nature Portfolio
publishDate	2018
url	https://doaj.org/article/a1584530b215410fbb759725c098982e
work_keys_str_mv	AT hengcongliu aparadoxofepidemicsbetweenthestateandparameterspaces AT muhuazheng aparadoxofepidemicsbetweenthestateandparameterspaces AT zonghualiu aparadoxofepidemicsbetweenthestateandparameterspaces AT hengcongliu paradoxofepidemicsbetweenthestateandparameterspaces AT muhuazheng paradoxofepidemicsbetweenthestateandparameterspaces AT zonghualiu paradoxofepidemicsbetweenthestateandparameterspaces
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A paradox of epidemics between the state and parameter spaces

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