  In this paper, we present a model to predict the spread of the Covid-19
epidemic and apply it to the specific case of Italy. We started from a simple
Susceptible, Infected, Recovered (SIR) model and we added the condition that,
after a certain time, the basic reproduction number $R_0$ exponentially decays
in time, as empirically suggested by world data. Using this model, we were able
to reproduce the real behavior of the epidemic with an average error of 5\%.
Moreover, we illustrate possible future scenarios, associated to different
intervals of $R_0$. This model has been used since the beginning of March 2020,
predicting the Italian peak of the epidemic in April 2020 with about 100.000
detected active cases. The real peak of the epidemic happened on the 20th of
April 2020, with 108.000 active cases. This result shows that the model had
predictive power for the italian case.
