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dc.contributor.author
Kröger, Martin
dc.contributor.author
Schlickeiser, Reinhard
dc.date.accessioned
2020-12-15T08:33:05Z
dc.date.available
2020-12-04T16:54:13Z
dc.date.available
2020-12-15T08:33:05Z
dc.date.issued
2020-12-18
dc.identifier.issn
1751-8113
dc.identifier.issn
1361-6447
dc.identifier.other
10.1088/1751-8121/abc65d
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/454765
dc.identifier.doi
10.3929/ethz-b-000454765
dc.description.abstract
We revisit the susceptible-infectious-recovered/removed (SIR) model which is one of the simplest compartmental models. Many epidemological models are derivatives of this basic form. While an analytic solution to the SIR model is known in parametric form for the case of a time-independent infection rate, we derive an analytic solution for the more general case of a time-dependent infection rate, that is not limited to a certain range of parameter values. Our approach allows us to derive several exact analytic results characterizing all quantities, and moreover explicit, non-parametric, and accurate analytic approximants for the solution of the SIR model for time-independent infection rates. We relate all parameters of the SIR model to a measurable, usually reported quantity, namely the cumulated number of infected population and its first and second derivatives at an initial time t = 0, where data is assumed to be available. We address the question of how well the differential rate of infections is captured by the Gauss model (GM). To this end we calculate the peak height, width, and position of the bell-shaped rate analytically. We find that the SIR is captured by the GM within a range of times, which we discuss in detail. We prove that the SIR model exhibits an asymptotic behavior at large times that is different from the logistic model, while the difference between the two models still decreases with increasing reproduction factor. This part A of our work treats the original SIR model to hold at all times, while this assumption will be relaxed in part B. Relaxing this assumption allows us to formulate initial conditions incompatible with the original SIR model.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
IOP Publishing
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
dc.subject
Statistical analysis
en_US
dc.subject
Epidemic spreading
en_US
dc.subject
Coronavirus
en_US
dc.subject
Extrapolation
en_US
dc.subject
SIR epidemic model
en_US
dc.subject
Asymptotic behavior
en_US
dc.subject
Analytic approximant
en_US
dc.title
Analytical solution of the SIR-model for the temporal evolution of epidemics. Part A: time-independent reproduction factor
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 4.0 International
dc.date.published
2020-11-24
ethz.journal.title
Journal of Physics A: Mathematical and Theoretical
ethz.journal.volume
53
en_US
ethz.journal.issue
50
en_US
ethz.journal.abbreviated
J. Phys. A: Math. Theor.
ethz.pages.start
505601
en_US
ethz.size
38 p.
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Bristol
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02160 - Dep. Materialwissenschaft / Dep. of Materials::02646 - Institut für Polymere / Institute of Polymers::03359 - Oettinger, Christian / Oettinger, Christian
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02160 - Dep. Materialwissenschaft / Dep. of Materials::02646 - Institut für Polymere / Institute of Polymers::03359 - Oettinger, Christian / Oettinger, Christian
en_US
ethz.date.deposited
2020-12-04T16:54:26Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2020-12-15T08:33:14Z
ethz.rosetta.lastUpdated
2021-02-15T22:31:44Z
ethz.rosetta.versionExported
true
ethz.COinS
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