Study on the effects of the restrictive measures for containment of the COVID-19 pandemic on the reproduction number R_t in Italian regions

Since November 6$^{\mathrm{th}}$, 2020, Italian regions have been classified according to four levels, corresponding to specific risk scenarios, for which specific restrictive measures have been foreseen. By analyzing the time evolution of the reproduction number $R_t$, we estimate how much different restrictive measures affect $R_t$, and we quantify the combined effect of the diffusion of virus variants and the beginning of the vaccination campaign upon the $R_t$ trend. We also compute the time delay between implementation of restrictive measures and the resulting effects. Three different models to describe the effects of restrictive measures are discussed and the results are cross-checked with two different algorithms for the computation of $R_t$.