Prediction of the time evolution of the Covid-19 Pandemic in Italy by a Gauss Error Function and Monte Carlo simulations

Ignazio Ciufolini; Antonio Paolozzi

In summary, starting from the nominal values of the daily data, we generated Gaussian distributions with 150 outcomes, with mean equal to the nominal values and with standard deviation equal to 10%. Then, for each of the 150 simulations, the residuals (corresponding to the cumulative positive cases of days) were fitted with a four parameter function of the type of the Gauss Error Function and we then determined the date of the flex with such fitted function for each simulation. Using the fitted function we also determined the date at which the number of daily positive cases will be less than a certain threshold that we have, for example, chosen to be 100. Finally we calculated the standard deviation of these 150 simulations. In Fig. 3 and Fig. 4 , we report the values (red dots) and the mean (horizontal line) of the Monte Carlo simulations respectively for the date of the flex and for the date of a substantial reduction in the number of daily positive cases. Using = 41 days (i.e., the number of daily diagnosed positive cases up to March 26, 2020), we thus obtained a standard deviation (1-sigma) of 1 day for the date of the flex and of 2.3 days for the date in which a substantial reduction of the daily cases would be below 100. This result corresponds to a probability of 68.2% that the date of the flex will be at a certain date plus or minus 1 day and that the date of a substantial reduction of the number of cases will be at a certain date plus or minus 2.3 days. A 2-sigma standard deviation will give a more robust probability of 95.4% of the day of the flex and of the day of a substantial reduction in the number of cases. The 2-sigma values correspond to plus or minus 2 days for the day of the flex and plus or minus 4.6 days for the day of a substantial reduction.