# Spatiotemporal Analysis of COVID-19 Incidence Data

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

## 3. Results

_{opt}for the number of clusters, we use the elbow criterion slightly modified (described in the same section), which gives k

_{opt}= 4 clusters. By cutting the tree in the dendrogram of Figure 4 (left panel) by the suitable horizontal line, we identify the elements of each of these four clusters. Precisely, we obtain: cluster1 = {1-Treviso, 2-Venice, 4-Vicenza}; cluster2 = {3-Padua}; cluster3 = {6-Belluno, 7-Verona}; cluster4 = {5-Rovigo} (the province numbers are the same as in Figure 2, right panel).

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Left: spatial distribution of the SARS-CoV-2 incidence in the period from 12 March to 15 May 2020, in all 1 km squared cells covering the Veneto region. Darker pixels correspond to lower intensity values. To increase the contrast of the image, a non-linear mapping (fourth root) is applied. Outlier values with very high intensity were reassigned through the 0.993 quantile (low-pass filter). Right: mathematical morphology opening operator applied to the image in the left panel followed by removal of “isolated” points. The values along x and y axes refer respectively to longitude and latitude.

**Figure 2.**Left: map of the SARS-CoV-2 municipalities incidences in Veneto relative to the period from 12 March to 15 May 2020, normalized by the corresponding populations at 31 December 2019. Intensity increases with respect to the normalized incidence. The intensities of a few municipalities with outlier values of the incidence were rescaled to increase the contrast of the map. The provinces boarders are thicker. Right: map of the Veneto provinces normalized incidences, obtained as the ratio between the sum of the total number of cases in all province municipalities and the corresponding total province population. The populations for the provinces (numbered from 1 to 7) are, respectively: 888,309; 851,663; 939,672; 862,363; 233,386; 201,972; 930,339.

**Figure 3.**Daily SARS-CoV-2 incidence in the seven provinces of Veneto, relative to the period from 12 March to 15 May 2020, normalized by the corresponding population at 31 December 2019, referred to 100,000 inhabitants. The continuous curve overlapped to the data is the best fit given by the extended logistic model.

**Figure 4.**Left: dendrogram from the hierarchical clustering analysis applied to the pairs (maximum value, maximum location) of the estimated curves of the daily SARS-CoV-2 normalized incidence of the seven Veneto provinces, shown in Figure 3. The numbers on the x-axis correspond to the province numbering in Figure 2, right panel. The numbers on the y-axis are instead the square root of the difference between the summation over the k clusters of the within cluster sum of squares, and the same quantity for k + 1 clusters, multiplied by √2. Right: provinces of the Veneto region with their municipalities, grouped according to the hierarchical clustering partition. The four province clusters identified are: cluster1 = {1-Treviso, 2-Venice, 4-Vicenza}; cluster2 = {3-Padua}; cluster3 = {6-Belluno, 7-Verona}; cluster4 = {5-Rovigo}. The greyscale intensity increases with the mean of the maximum value of the estimated curves in Figure 3, among the provinces belonging to the same cluster.

**Figure 5.**In panel (

**a**) we show the linear fit of the maximum value of the province incidence curves in Figure 3 vs. the corresponding population density. In panel (

**b**), the provinces are grouped according to the clusters shown in the right panel of Figure 4. The determination coefficients are also shown. The acronyms B, Ver, Ven, T, Vi, P and R stand for Belluno, Verona, Venezia, Treviso, Vicenza, Padua and Rovigo, respectively.

**Figure 6.**Survival function of the Veneto municipalities incidence in the period from 12 March to 15 May 2020, in a loglog scale. The best fit by the tapered Pareto model is shown by a continuous black line.

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**MDPI and ACS Style**

Spassiani, I.; Sebastiani, G.; Palù, G.
Spatiotemporal Analysis of COVID-19 Incidence Data. *Viruses* **2021**, *13*, 463.
https://doi.org/10.3390/v13030463

**AMA Style**

Spassiani I, Sebastiani G, Palù G.
Spatiotemporal Analysis of COVID-19 Incidence Data. *Viruses*. 2021; 13(3):463.
https://doi.org/10.3390/v13030463

**Chicago/Turabian Style**

Spassiani, Ilaria, Giovanni Sebastiani, and Giorgio Palù.
2021. "Spatiotemporal Analysis of COVID-19 Incidence Data" *Viruses* 13, no. 3: 463.
https://doi.org/10.3390/v13030463