Figure 1

Monitoring regional reproduction numbers (R_t’s): funnel plots and control chart. Panels a-d show the Italian regional R_t’s (colour-coded circles, see Supplementary {1} for the legend), plotted against the infectious cases at four selected times. When the epidemic evolution is homogenous across regions, differences between R_t’s are exclusively due to natural statistical variability and the circles are expected to lie inside the black alarm limits in 99.8% of the cases. The alarm limits have the shape of a funnel because the variance of the estimated R_t is inversely proportional to the number of infectious cases. The central dashed line represents the average R_t. A circle is out of statistical control if it lies outside the black funnel. Out-of-control circles might therefore reveal anomalies that disrupt the homogeneity between regions. In (a–d), the majority of the points, lying in the funnel, are essentially indistinguishable and therefore not even named. On 22 December 2021, Lombardia (dark red) crossed the alarm limit and on 24 December 2021 it was completely outside the upper alarm limit. As confirmed by a survey by the Italian National Institute of Health, Lombardia was the first Italian region to be colonized by the Omicron variant. As the other regions were colonized too, the distribution of their R_t’s moved upward and, on 2 January 2022, Lombardia was again inside the funnel. The trend can be monitored by plotting the standardized R_t’s on a Bonferroni control chart with \(\pm 3\).09 (e), where the introduction of the Omicron variant in Lombardia in mid-December is clearly visible.