[IPOL discuss] [IPOL announce] new article: A Daily Measure of the SARS-CoV-2 Effective Reproduction Number for all Countries

[announcements about the IPOL journal]

A new article is available in IPOL: https://www.ipol.im/pub/art/2020/304/

Tahar Zamene Boulmezaoud, Luis Álvarez, Miguel Colom, and Jean-Michel 
Morel,
A Daily Measure of the SARS-CoV-2 Effective Reproduction Number for all 
Countries,
Image Processing On Line, 10 (2020), pp. 191–210.
https://doi.org/10.5201/ipol.2020.304

Abstract
We describe a transparent method calculating an 'effective reproduction 
number (ERN)' from the daily count (incidence) of newly detected cases 
in each country, in the EU and in each US state. We aim at getting a 
result as faithful as possible to the observed data, which are very 
noisy. The noise, being specific of administrations, shows a seven days 
period. Hence the incidence curve is first filtered by a seven days mean 
or median filter.
Then the ERN is computed by a classic reproduction formula due to 
Nishiura. To do so requires knowledge of the serial interval function 
Phi(s) which models the time between the onset of symptoms in a primary 
case and the onset of symptoms in secondary cases, or equivalently the 
probability that a person confirmed infected today was actually infected 
s days earlier by another confirmed infected person. We use and compare 
several recently proposed evaluations of Phi, and verify that their 
variation has moderate practical incidence on the evaluation of the ERN. 
The method we present derives from Nishiura's formula but we prove that 
for the adequate choice of parameters it is identical to one of the 
methods proposed by the classic EpiEstim (Estimate Time Varying 
Reproduction Numbers from Epidemic Curves) software. We find that the 
same method can be applied to compute an effective reproduction number 
from the daily death count, which yields therefore another prediction of 
the expansion of the pandemic. Although this application has no clear 
theoretical justification, we find good experimental fit of the ERN 
curves obtained from the incidence and from the death curve, up to a 
time shift. In most countries, both curves appear to be similar, with a 
time delay that depends on each country's detection and administrative 
processing delays. Both ERNs can be consulted daily online in the demo 
tag associated with this paper. We refer the readers to the online demo 
to experiment by themselves. In the case of France, an ERN based on 
hospitalizations, new entries in ICU's and deaths at hospitals is also 
computed daily.


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