Spatiotemporal evolution of COVID-19 in Portugal's Mainland with self-organizing maps

Abstract

Background: Self-Organizing Maps (SOM) are an unsupervised learning clustering and dimensionality reduction algorithm capable of mapping an initial complex high-dimensional data set into a low-dimensional domain, such as a two-dimensional grid of neurons. In the reduced space, the original complex patterns and their interactions can be better visualized, interpreted and understood.

Methods: We use SOM to simultaneously couple the spatial and temporal domains of the COVID-19 evolution in the 278 municipalities of mainland Portugal during the first year of the pandemic. Temporal 14-days cumulative incidence time series along with socio-economic and demographic indicators per municipality were analyzed with SOM to identify regions of the country with similar behavior and infer the possible common origins of the incidence evolution.

Results: The results show how neighbor municipalities tend to share a similar behavior of the disease, revealing the strong spatiotemporal relationship of the COVID-19 spreading beyond the administrative borders of each municipality. Additionally, we demonstrate how local socio-economic and demographic characteristics evolved as determinants of COVID-19 transmission, during the 1st wave school density per municipality was more relevant, where during 2nd wave jobs in the secondary sector and the deprivation score were more relevant.

Conclusions: The results show that SOM can be an effective tool to analysing the spatiotemporal behavior of COVID-19 and synthetize the history of the disease in mainland Portugal during the period in analysis. While SOM have been applied to diverse scientific fields, the application of SOM to study the spatiotemporal evolution of COVID-19 is still limited. This work illustrates how SOM can be used to describe the spatiotemporal behavior of epidemic events. While the example shown herein uses 14-days cumulative incidence curves, the same analysis can be performed using other relevant data such as mortality data, vaccination rates or even infection rates of other disease of infectious nature.

Keywords: COVID-19; Geo-Spatial Analysis; SARS-CoV-2; Self-organizing maps; Socio-economic determinants of disease.

Fig. 1

Schematic representation of: a the SOM architecture; b main steps during SOM training

Fig. 2

QE and TE for all the 16,400 SOM models evaluated during the SOM parameterization (blue filled circles) for the five periods considered during the first year of pandemic: a 1st emergency state; b summer season; c sept-oct of 2020; d 2nd wave of COVID-19; e Holyday season. The model with the smallest QE and TE is highlighted in red

Fig. 3

Schematic representation of the geographical representation of the SOM output feature space using projected coordinate system for each municipality

Fig. 4

14-days cumulative incidence curves for all the municipalities considering: a 1st emergency state; b summer season; c sept-oct of 2020; d 2nd wave of COVID-19; e Holyday season. Each color represents a different municipality as shown in Figs. 5 and 6. Black thick curve represents the national 14-days cumulative incidence curve

Fig. 5

U-Matrices obtained with the SOM applied to data corresponding to the: a 1st emergency state; b summer season; c sept-oct of 2020; d 2nd wave of COVID-19; e Holyday season. Each color represents a different municipality as shown in Figs. 4 and 6

Fig. 6

Geographical projection of the cluster obtained from the SOM models: a 1st emergency state; b summer season; c sept-oct of 2020; d 2nd wave of COVID-19; e Holyday season. Each color represents a different municipality

Fig. 7

Components plane for the period corresponding to the 1st emergency state

Fig. 8

Components plane for the period corresponding to the summer season

Fig. 9

Component planes for the period corresponding to sept–oct of 2020

Fig. 10

Component planes for the period corresponding to the 2nd wave of COVID-19

Fig. 11

Component planes for the period corresponding to the Holyday season