# Gaussian Parameters Correlate with the Spread of COVID-19 Pandemic: The Italian Case
## 4 Conclusions and Future Perspectives  
A simple model constituted by a Gaussian mixture, defined taking into account anti-contagion control measures, has been used to fit the growth rate of COVID-19 affected, deceased and recovered people in Italy. The statistical correlation between considered pair of variables allowed us inferring the variation of the virus diffusion in correspondence of the effect of well identified events during the pandemic spread in Italy. Furthermore, our GGR model allowed to reproduce the cumulative distribution functions of total cases, deaths and recovers as well as their daily distribution in terms of probability density functions, giving information about the statistical distribution of events and conferring a short-term predictive power to the model that is unfortunately limited to few days. However, in terms of survival analysis, an interesting prediction has been obtained. To this purpose we compared the trend of susceptible and vaccinated people in order to establish a time interval within which all people will be infected or vaccinated (with at least one dose) and/or the definitive time of the end of pandemic in Italy when all people will be infected or vaccinated after the two doses. Figure 7 shows on a log-lin scale the number of susceptible people (black squares, obtained by subtracting the cumulative cases from the total of the population) and those of vaccinated people (red and blue symbols for people vaccinated with a single or double doses, respectively) as a function of time. By a simple data extrapolation, we can locate the first mentioned time interval around the mid of July and the definitive end of pandemic in Italy one month later, around the mid of August, if the vaccination rate remains the same. Figure 7: Semi-logarithmic plot of the intersection points between trends of Susceptible and vaccinated people with first (red data) and second (blue data) doses (data available from [48]). Dotted lines correspond to data extrapolation for evaluating the intersection that may mark the end of the pandemic in Italy. Finally, for a complete description of the whole pandemic until the foreseen end (mid of August), our model predicts the occurrence of one, two at most, additional soft events during which we must cohabit with the virus aiming to achieve the herd immunity. Our estimation for new soft events refers to the time needed to reach the herd immunity if the vaccination rate remains unchanged. If so, only a low-intensity additional Gaussian band would be needed to fit the data up to the mid of August. This prediction cannot consider possible effects due to new virus variants or other uncontrolled events. Hence, in the near future, we will continue monitoring the virus spreading and running our model to confirm its actual prediction and to further test its ability to reproduce COVID-19 data including any other unexpected circumstances. Conceptualization, C.C., A.S. and E.F.; methodology, C.C. and E.F.; data curation, A.S.; writing--review and editing, C.C., A.S. and E.F. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Publicly available datasets were analyzed in this study.