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\title{Supplementary Informations}


\maketitle

\subsection*{Sample distribution}

In Table \ref{tab:region} we show the distribution of participants for each Italian region across the seven waves of data collection.
\begin{table}[ht]
\caption{Distribution of participants per wave and Italian regions.}
    
    \centering
    \includegraphics[width=\textwidth]{SI_Table1.pdf}
    \label{tab:region}
\end{table}



\subsection*{Contact matrices}
The detailed contact matrices for the different settings, waves and the zones are shown in Figures (\ref{fig:comix_cm_settings},\ref{fig:comix_cm_wave},\ref{fig:comix_cm_zone}) respectively.



\begin{figure}
\caption{Contact matrices by waves (1 - 7).}
\includegraphics[width=\textwidth]{SI_Figure1.pdf}
\centering
\label{fig:comix_cm_wave}
\end{figure}


\begin{figure}
\caption{Contact matrices by zone.}
\includegraphics[width=\textwidth]{SI_Figure2.pdf}
\centering
\label{fig:comix_cm_zone}
\end{figure}

\begin{figure}
\caption{Contact matrices by settings.}
\includegraphics[width=\textwidth]{SI_Figure3.pdf}
\centering
\label{fig:comix_cm_settings}
\end{figure}

\subsection*{$R_0$ computation and statistical test}

In Figure \ref{fig:R0_supp} we show an age sensitivity analysis using different susceptibility (a) and infectivity (h) values taken from literature. The formula to compute $R_0$ is:

\begin{equation}
    R_{0_{\tau}} = R_{0_{ref}} \frac{\rho(diag(\mathbf{a}) M_{\tau} diag(\mathbf{h}))}{\rho(diag(\mathbf{a}) M_{P} diag(\mathbf{h}))}
\end{equation}

In Figure \ref{fig:R0_supp}-a) we used a = [0.79 0.86 0.8  0.82 0.8 ] and h = [0.59 0.7  0.76 0.9  0.99] from \cite{Franco2022a} for Belgium, in figure \ref{fig:R0_supp}-b) we used a = [0.79 0.86 0.8  0.82 0.8 ] and h = [0.64 0.67 0.7  0.75 0.84] from \cite{davies2020agea}, while figure 5-c) is the same shown in the main article where we used homogeneous values equal to 1 (i.e. age independent susceptibility and infectivity). 
As one can note, the differences between the 3 figures are extremely small because the largest differences in susceptibility and infectivity are between adults and children. However, the latter are not included in our analysis and thus, as one can note, the differences between the 3 figures are extremely small. Furthermore, the couples of vectors a and h used in Figure \ref{fig:R0_supp}-a) and \ref{fig:R0_supp}-b) are computed for different countries. For this reason, we kept Figure \ref{fig:R0_supp}-c) with homogeneous susceptibility and infectivity.

The differences between the matrices in the different zones were measured considering the principal eigenvalue of the matrix as the representative metric. In particular, we computed the t-test and the ks-test to compare the 10000 bootstrap realization of the principal eigenvalues. The distributions of the $R_0$ samples for each zone is shown in Fig \ref{fig:comix_dist}. The results show that the matrices are significantly different from one zone to another $p<0.0001$.

\begin{figure}
\caption{Basic reproduction number for each zone. In Figure a) we used age-dependent susceptibility and infectivity vectors from \cite{Franco2022a}, in b) we used age-dependent susceptibility and infectivity vectors from \cite{davies2020agea} and in c) we assumed homogeneous values equal to 1 for all age groups.}
\includegraphics[width=\textwidth]{SI_FIgure_5.pdf}
\centering

\label{fig:R0_supp}
\end{figure}

\begin{figure}[ht]
\caption{Distribution of eigenvalues for different waves and zones, 10000 bootstrap.}

\includegraphics[width=\textwidth]{SI_Figure4.pdf}
\centering
\label{fig:comix_dist}
\end{figure}
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