Analysis of the prediction of the 2021 time-evolution of the COVID-19 Pandemic in Italy using a Planck's distribution (preprint)

In a previous paper we studied the time evolution of the Covid-19 pandemic in Italy during the first wave of 2020 using a number of distribution laws. We concluded that the best distribution law to predict the evolution of the pandemic, if basic conditions of the pandemic (such as distancing measures, use of masks, start of schools, intensive use of public transportation, beginning and end of holidays, vaccination campaign and no significant onset of new Covid variants) do not appreciably change, is a distribution of the type of Plancks law with three parameters. In our 2020 study we did not use the number of daily positive cases in Italy but the ratio of daily positive cases per number of daily tests, ratio today sometimes referred to as: "positivity rate". We showed that, if basic conditions do not change, the Plancks distribution with three parameters provides very good predictions of the positivity rate about one month in advance. In particular, in a second paper, using the Plancks distribution with three parameters, we predicted, about one month in advance, the spread of the pandemic in Italy during the Christmas 2020 holidays with an error of a few percent only. We then study the present (September 2021) evolution of the pandemic in Italy and we show that the Plancks distribution, based on the data of July and August, predicts well the evolution of the pandemic. In particular, we show that the peak of the positivity rate was predicted to occur approximately around the middle of August and that the agreement of this Plancks function (obtained fitting the data up to 10 July 2021) and the positivity rate observed after 5 weeks, on 12 September 2021 is very good. However, the end of the Italian holidays and the start of all the activities including schools, intensive use of public transportation and further changes in distancing measures may cause a discrepancy of the predicted trend of the positivity rate of the pandemic with respect to the real observed values.

Prediction of evolution of the second wave of Covid-19 pandemic in Italy (preprint)

A relevant problem in the study of the Covid-19 pandemic is the study of its temporal evolution. Such evolution depends on a number of factors, among which the average rate of contacts between susceptible and infected individuals, the duration of infectiousness and the transmissibility, that is the probability of infection after a contact between susceptible and infected individuals. In a previous study, we analyzed the potentiality of a number of distributions to describe the evolution of the pandemic and the potentiality of each distribution to mathematically predict the evolution of the pandemic in Italy. Since the number of daily tests was changing and increasing with time, we used the ratio of the new daily cases per swab. We considered distributions of the type of Gauss (normal), Gamma, Beta, Weibull, Lognormal and in addition of the type of the Planck blackbody radiation law. The Planck law, describing the amount of energy of the electromagnetic radiation emitted by a black body at each wavelength or at each frequency, marked in 1900 the beginning of Quantum Mechanics. The result of our analysis was that, among the considered distributions, the Planck law has the best potentiality to mathematically predict the evolution of the pandemic and the best fitting capability. In this paper, we analyze the time evolution of this second wave of Covid-19 pandemic in Italy. In this study there is also an attempt to account for the effects of the governmental containment measures.

An improved mathematical prediction of the time evolution of the Covid-19 Pandemic in Italy, with Monte Carlo simulations and error analyses (preprint)

We present an improved mathematical analysis of the time evolution of the Covid-19 pandemic in Italy and a statistical error analyses of its evolution, including Monte Carlo simulations with a very large number of runs to evaluate the uncertainties in its evolution. A previous analysis was based on the assumption that the number of nasopharyngeal swabs would be constant. However the number of daily swabs is now more than five times what it was when we did our previous analysis. Therefore, here we consider the time evolution of the ratio of the new daily cases to number of swabs, which is more representative of the evolution of the pandemic when the number of swabs is increasing or changing in time. We consider a number of possible distributions representing the evolution of the pandemic in Italy and we test their prediction capability over a period of up to four weeks. The results show that a distribution of the type of Planck black body radiation law provides very good forecasting. The use of different distributions provides an independent possible estimate of the uncertainty. We then consider five possible trajectories for the number of daily swabs and we estimate the potential dates of a substantial reduction in the number of new daily cases. We then estimate the spread in a substantial reduction, below a certain threshold, of the daily cases per swab among the Italian regions. We finally perform Monte Carlo simulations with 25000 runs to evaluate a random uncertainty in the prediction of the date of a substantial reduction in the number of diagnosed daily cases per swab.

A Mathematical prediction of the time evolution of the Covid-19 pandemic in some countries of the European Union using Monte Carlo simulations (preprint)

In this paper we study the statistical evolution in time of the Covid-19 pandemic in Spain, Italy, Germany, Belgium, The Netherlands, Austria and Portugal, i.e., the countries of the European Union (EU) that have a number of positive cases higher than 12 thousand at April 7, 2020. France is the third country of the EU for number of cases but a jump in the data on April 3, 2020 does not allow, at least for the moment, to have a reliable prediction curve. The analysis is based on the use of a function of the type of a Gauss Error Function, with four parameters, as a Cumulative Distribution Function (CDF). A Monte Carlo analysis is used to estimate the uncertainty. The approach used in this paper is mathematical and statistical and thus does not explicitly consider a number of relevant issues, including number of nasopharyngeal swabs, mitigation measures, social distancing, virologic, epidemiological and models of contamination diffusion.

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

In this paper are presented 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 as a Cumulative Distribution Function (CDF). 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, i.e., to the change in sign of its second derivative (that is 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 then performed 150 Monte Carlo simulations in the attempt to have a more robust prediction of the day of the above-mentioned peak and of the day of the substantial decrease of the number of daily positive cases. Although, official data have been used, these predictions are obtained with a heuristic approach, since those predictions are based on statistical approach and do not take into account either a number of relevant issues (such as medical, social distancing, virologic, epidemiological, etc.) or models of contamination diffusion.