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.