Statistical and network-based analysis of Italian COVID-19 data: communities detection and temporal evolution

Marianna Milano; Mario Cannataro

In this section, we analyze the evolution of the Italian COVID-19 networks data. Figure 2 shows the evolution of Hospitalised with Symptoms network over five weeks. Figure 2 (a) reports the network that represents the behaviour of regions respect to number of hospitalised patients up to March 29, whereas Figure 2 (b), (c), (d), (e), (f) represent the networks on each single week. It is to notice, the network structure changes according to the analyzed time interval. At the end of 35th day, the network has all nodes connected with exception of a single node that represent the Basilicata region. Furthermore, it is possibile to highlight different community structures consisting of groups of regions with similar trends. Figure 12 (a) reports five communities: the first one consists of Basilicata; the second one is composed by Piemonte, Marche, Emilia, Lombardia, Veneto; the third one is composed by Liguria, Lazio, Toscana; the fourth one is formed by Campania, Puglia, Sicilia, Abruzzo, Valle d' Aosta, Friuli, Trento, Bolzano; the last one is composed by Umbria, Sardegna, Calabria, Molise. Figure 3 represents the evolution of Intensive Care network. It is possible to notice that Lombardia and Veneto, that are the most affected region by Coronavirus disease with high number hospitalised in Intensive Care Units, are disconnected in the first week. In the second week, Lombardia and Veneto are connected by an edge that represents a level of similarity, whereas in the fifth week Veneto is linked with Emilia and Lombardia and this group of regions becomes a disconnected component among with other regions. Thus, while initially Lombardia and Veneto showed a similar trend of Intensive Care data, after Veneto moved far from Lombardia trend. Furthermore, by analyzing the communities in the Intensive Care network (Figure 12 (b)), it is possible to evidence four subgraphs formed by (i) Lombardia and Veneto, (ii) Umbria and Lazio, (iii) Marche, Emilia, Piemonte, Toscana and (iv) a large module formed by Campania, Sicilia, Sardegna, Abruzzo, Umbria, Calabria, Basilicata, Bolzano, Valle d'Aosta, Friuli, Trento, Molise. Figure 4 show the Total Hospitalised network evolution. Starting form the first week, the structure of the network has two disconnected nodes representing Lombardia and Veneto, whereas in the second week the network evolves by presenting a single disconnected node that represent Emilia, and two connected nodes, Lombardia and Veneto, which in turn are disconnected from dense subgraph. In the third and fourth week the network structure presents all connected components, and high number of nodes result disconnected in the fifth week. Finally, all re-gions are connected in the final network. By analyzing the communities detected in Total Hospitalised network (Figure 12 (c)), it is possible to notice a similarity with those extracted by Hospitalised with Symptoms networks. In fact, there is a correspondence among three communities: (i) Basilicata and Piemonte, (ii) Marche, Emilia, Lombardia, (iii) Veneto and Liguria, Lazio, Toscana. This means that those regions that form the tree communities present the same behaviour according to the number of the hospitalised patients with symptoms and the total number of hospitalised patients. Figure 5 shows the evolution of Home Isolation network over five weeks. In first week, Lombardia, Veneto and Emilia show a different trend of the number of subjects in isolation at home, both them and also compared to