| An analytic evaluation of the peak time of a disease allows for the installment of effective epidemicprecautions. Recently, an explicit analytic, approximate expression (MT) for the peak time of thefraction of infected persons during an outbreak within the susceptible–infectious–recovered/removed(SIR) model had been presented and discussed (Turkyilmazoglu, 2021). There are three existingapproximate solutions (SK-I, SK-II, and CG) of the semi-time SIR model in its reduced formulation thatallowonetocomeupwithdifferentexplicitexpressionsforthepeaktimeoftheinfectedcompartment(Schlickeiser and Kröger, 2021; Carvalho and Gonçalves, 2021). Here we compare the four expressionsfor any choice of SIR model parameters and find that SK-I, SK-II and CG are more accurate than MT as long as the amount of population to which the SIR model is applied exceeds hundred by far(countries, ss, cities). For small populations with less than hundreds of individuals (families, smalltowns),however,theapproximantMToutperformstheotherapproximants.Tobeabletocomparethevariousapproaches,weclarifytheequivalencebetweenthefour-parametricdimensionalSIRequationsand their two-dimensional dimensionless analogue. Using Covid-19 data from various countries andsources we identify the relevant regime within the parameter space of the SIR model.
for LaTeX users @article{MKroger2021-425,
author = {M. Kr\"oger and M. Turkyilmazoglu and R. Schlickeiser},
title = {Explicit formulae for the peak time of an epidemic from the SIR model. Which approximant to use?},
journal = {Physica D},
volume = {425},
pages = {132981},
year = {2021}
}
\bibitem{MKroger2021-425} M. Kr\"oger, M. Turkyilmazoglu, R. Schlickeiser,
Explicit formulae for the peak time of an epidemic from the SIR model. Which approximant to use?,
Physica D {\bf 425} (2021) 132981.MKroger2021-425
M. Kr\"oger, M. Turkyilmazoglu, R. Schlickeiser
Explicit formulae for the peak time of an epidemic from the SIR model. Which approximant to use?
Physica D,425,2021,132981 |
mk@mat.ethz.ch
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