Mathematical prediction of the time evolution of the COVID-19 pandemic in Italy by a Gauss error function and Monte Carlo simulations

In this paper are presented mathematical predictions on the evolution in time of the number of positive cases in Italy of the COVID-19 pandemic based on official data and on the use of a function of the type of a Gauss error function, with four parameters, as a cumulative distribution function. We have analyzed the available data for China and Italy. The evolution in time of the number of cumulative diagnosed positive cases of COVID-19 in China very well approximates a distribution of the type of the error function, that is, the integral of a normal, Gaussian distribution. We have then used such a function to study the potential evolution in time of the number of positive cases in Italy by performing a number of fits of the official data so far available. We then found a statistical prediction for the day in which the peak of the number of daily positive cases in Italy occurs, corresponding to the flex of the fit, that is, to the change in sign of its second derivative (i.e., the change from acceleration to deceleration), as well as of the day in which a substantial attenuation of such number of daily cases is reached. We have also analyzed the predictions of the cumulative number of fatalities in both China and Italy, obtaining consistent results. We have then performed 150 Monte Carlo simulations to have a more robust prediction of the day of the above-mentioned peak and of the day of the substantial decrease in the number of daily positive cases and fatalities. Although official data have been used, those predictions are obtained with a heuristic approach since they are based on a statistical approach and do not take into account either a number of relevant issues (such as number of daily nasopharyngeal swabs, medical, social distancing, virological and epidemiological) or models of contamination diffusion.