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

By considering the cumulative diagnosed positive cases of Covid-19 infections available in the web site of the Italian "Ministero della Salute" 1 , World Health Organization 2 and Worldometer 3 , we found that they can be well approximated by a Cumulative Distribution Function (CDF) of the type of the Gauss Error Function, that is the integral of a normal, Gaussian distribution. Incidentally, such behavior is similar to the behavior of the incubation time of the seasonal influenza 4 . By positive cases we mean the positive cases actually diagnosed plus, for future days, the positive cases that we expect to be diagnosed. In fact it is well known among the virologists that the actual number of positive cases is much higher than the diagnosed ones 5 . However, it is assumed the diagnosed cases are a good statistical representation of the entire population of the positive cases. In Fig. 1 , we report the result of our fit of the cumulative diagnosed positive cases in China. We have then applied such a CDF to study the evolution in time of the number of positive cases in Italy, in the attempt to possibly, statistically, predict the peak in the number of daily positive cases and the possible date of a substantial decrease in the number of daily positive cases. Finally, in section 4 we have performed a number of Monte Carlo simulations to get a more robust prediction of both the date of the peak in the number of positive cases each day and the date after which the number of new positive cases is below a certain threshold.