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

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.

Geostatistical COVID-19 infection risk maps for Portugal.

The rapid spread of the SARS-CoV-2 epidemic has simultaneous time and space dynamics. This behaviour results from a complex combination of factors, including social ones, which lead to significant differences in the evolution of the spatiotemporal pattern between and within countries. Usually, spatial smoothing techniques are used to map health outcomes, and rarely uncertainty of the spatial predictions are assessed. As an alternative, we propose to apply direct block sequential simulation to model the spatial distribution of the COVID-19 infection risk in mainland Portugal. Given the daily number of infection data provided by the Portuguese Directorate-General for Health, the daily updates of infection rates are calculated by municipality and used as experimental data in the geostatistical simulation. The model considers the uncertainty/error associated with the size of each municipality's population. The calculation of daily updates of the infection risk maps results from the median model of one ensemble of 100 geostatistical realizations of daily updates of the infection risk. The ensemble of geostatistical realizations is also used to calculate the associated spatial uncertainty of the spatial prediction using the interquartile distance. The risk maps are updated daily and show the regions with greater risks of infection and the critical dynamics related to its development over time.