Table 1.

Total cases over population (per 10 000 inhabitants) — 3 clusters memberships.

	Region	Model with no spatial penalty ($\gamma =0$)			Model with spatial penalty ($\gamma ={\gamma }_{opt}$)
		Cluster 1	Cluster 2	Cluster 3	Cluster 1	Cluster 2	Cluster 3
		Piedmont	Lazio	Basilicata	Piedmont	Lazio	Calabria
1	Piedmont	1.000	0.000	0.000	1.000	0.000	0.000
2	Aosta Valley	0.646	0.179	0.174	0.697	0.154	0.150
3	Lombardy	0.989	0.006	0.005	0.992	0.004	0.003
4	Trentino–South Tyrol	0.910	0.049	0.041	0.936	0.035	0.029
5	Veneto	0.759	0.134	0.106	0.849	0.083	0.068
6	Friuli-Venezia Giulia	0.622	0.266	0.112	0.688	0.222	0.089
7	Liguria	0.923	0.055	0.023	0.881	0.087	0.032
8	Emilia-Romagna	0.814	0.137	0.049	0.784	0.160	0.056
9	Tuscany	0.042	0.911	0.047	0.095	0.860	0.045
10	Umbria	0.070	0.878	0.052	0.031	0.953	0.016
11	Marche	0.010	0.957	0.034	0.019	0.964	0.017
12	Lazio	0.000	1.000	0.000	0.000	1.000	0.000
13	Abruzzo	0.001	0.995	0.005	0.000	0.999	0.000
14	Molise	0.001	0.044	0.955	0.013	0.943	0.044
15	Campania	0.025	0.943	0.032	0.020	0.964	0.015
16	Apulia	0.005	0.289	0.706	0.018	0.910	0.072
17	Basilicata	0.000	0.000	1.000	0.044	0.433	0.523
18	Calabria	0.024	0.059	0.918	0.000	0.000	1.000
19	Sicily	0.414	0.295	0.291	0.376	0.279	0.345
20	Sardinia	0.160	0.213	0.627	0.027	0.036	0.937