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

Ciufolini, I.; Paolozzi, A.

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 (i.e., distancing measures, start of schools, intensive use of public transportation, beginning and end of holidays, new vaccines, spread of new Covid variants) of the pandemic do not appreciably change, is a distribution of the type of Planck's 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 Planck's distribution with three parameters provides very good predictions of the positivity rate about one month in advance. In a second paper, using the Planck's distribution with three parameters, we predicted, about one month in advance, the spread of the pandemic in Italy during the Christmas holidays. Here we show that indeed in our second paper the spread of the pandemic in Italy, after one month, was well predicted using the Planck's distribution with an error of a few percent only. We then study the present (beginning of September) evolution of the pandemic in Italy and we show that the Planck's distribution, based on the data of July and August, predicts well the evolution of the pandemic. We then show that, at present, the peak of the ratio of the positivity rate was reached during the second part of August. However, the end of the Italian holidays and the start of schools, intensive use of public transportation and further distancing measures may change again the trend of the positivity rate of the pandemic.