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A surprisingly simple way to assess the reproduction number of any national corona epidemic

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Abstract

The KORMOD model of the corona epidemic is ridiculously simple - rich in terms of output, but undemanding in terms of input. The only information used is the daily incidence of new positive coronavirus tests. The prevalence of infectious people is calculated as the sum of all new infections (the incidences) 3 to 9 days back. The daily incidence rate = incidence/prevalence = new infections per infectious person per day. The reproduction number (R) is 7 times the daily incidence rate, since the infectious period is 7 days long. Alternatively, a gamma distribution with mean 6.5 or 4.8 days is used for the infection-to-infection time. We apply the model to plot the reproduction numbers of the USA, UK, Germany, Russia, India, Turkey, Brazil, Chile, Sweden and Norway.
A surprisingly simple way to assess the
reproduction number
of any national corona epidemic
Lasse Fridstrøm
May 15, 2020
Page
KORMOD
Ridiculously simple model: only information used is the daily incidence
of new positive coronavirus tests.
The prevalence of infectious people is the sum of all new infections (the
incidences) 3 to 9 days back (7-day period).
This is tantamount to assuming a rectangular infection-to-infection time
distribution with mean 6.5 days.
The daily incidence rate = incidence/prevalence = new infections per
infectious person per day
Reproduction number (R) is 7 times daily incidence rate.
Alternatively, gamma distributions with mean 6.5 or 4.8 days are used
for infection-to-infection time, as suggested by the Imperial College in
their March 30 report or by Ferretti et al. (2020), respectively.
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Rectangular or gamma distributed infection-to-infection time
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Incidence rate in Norway under three different assumptions
regarding infection-to-infection time distribution
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Problem: underreporting
Only a small share of infections are discovered by testing. There
is measurement error (underreporting).
But the error affects both numerator and denominator in
incidence-to-prevalence ratio.
If the relative measurement error is constant, the ratio
incidence/prevalence, and hence R, is correctly estimated.
If the relative measurement error changes fast, sizable bias may
arise.
Under normal conditions, bias will be moderate.
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Reporting probability: four numerical examples
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Sensitivity analysis: true incidence rate by degree of reporting
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R estimates for
UK, USA, Sweden, Norway, Germany
Data source: Miscellaneous
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R estimates for
USA, India, Brazil, Russia, Turkey, Chile
Data source: Covid-19 Dashboard of Johns Hopkins University
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Thanks for your attention!
Stay safe!
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