Until today, numerous models have been formulated to predict the spreading of Covid-19. Among them, the actively discussed susceptible-infected-removed (SIR) model is one of the most reliable. Unfortunately, many factors (i.e., social behaviors) can influence the outcomes as well as the occurrence of multiple contributions corresponding to multiple waves. Therefore, for a reliable evaluation of the conversion rates, data need to be continuously updated and analyzed. In this work, we propose a model using Gaussian functions, coming from the solution of an ordinary differential equation representing a logistic model, able to describe the growth rate of infected, deceased and recovered people in Italy. We correlate the Gaussian parameters with the number of people affected by COVID-19 as a function of the large-scale anti-contagion control measures strength, and also of vaccines effects adopted to reach herd immunity. The superposition of gaussian curves allow modeling the growth rate of the total cases, deceased and recovered people and reproducing the corresponding cumulative distribution and probability density functions. Moreover, we try to predict a time interval in which all people will be infected or vaccinated (with at least one dose) and/or the time end of pandemic in Italy when all people have been infected or vaccinated with two doses.

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