On the COVID-19 outbreak in Italy

Filippo Colomo

(INFN, Florence & DIPFA, UniFI)

The subsequent analysis is based on the data provided by Protezione Civile.
Data timeseries start on February 24, 2020 (hereafter, days `-5 of March').
The analysis has been done using Wolfram Mathematica. The code we used is available here.
We fit cumulative data (cumulative number of confirmed cases, or of fatalities) with the logistic function (blue) and the error function (green).
We fit daily data (number of infectious daily fatalities) with the logistic distribution (blue) and the normal distribution (green).
In the best fit procedure, we assume that data of magnitude n are affected by an error ± √ n .
Only the first part of the data (black dots), till the date indicated in each plot, is used for the fit.
Remaining data (red dots) are NOT used for the fit, but just reported as a check of the predictivity of the two curves.
For each plot we report:
- "date" is the date of the best fit: only data earlier than "date" have been used (NB: "33 March" means "2 April", etc.);
- "t₀" is the best fit value for the date of the peak (or, for cumulative data, of the inflection point), for the considered quantity;
- "A" is the best fit value at peak (or, for cumulative data, at inflection point), for the considered quantity.
The analysis suggests that, when the outbreak is still at its early stages (say, before its peak), fits of available empirical data by the error function (or normal distribution) could be more predictive than those by the logistic function (or logistic distribution, respectively).
Note added on 2 April 2020: concerning daily fatalities, whose peak is presumably already behind us, in the most recent fit, the logistic distribution is starting to perform better than the Gaussian distribution.
Note added on 3 April 2020: Having now sufficient data, we have made a check of the compliance of fits made one/two/three weeks ago with subsequent data.