Modeling the geospatial evolution of COVID-19 using spatio-temporal convolutional sequence-to-sequence neural networks

Europe was hit hard by the COVID-19 pandemic and Portugal was one of the most affected countries, having suffered three waves in the first twelve months. Approximately between Jan 19th and Feb 5th 2021 Portugal was the country in the world with the largest incidence rate, with 14-days incidence rates per 100,000 inhabitants in excess of 1000. Despite its importance, accurate prediction of the geospatial evolution of COVID-19 remains a challenge, since existing analytical methods fail to capture the complex dynamics that result from both the contagion within a region and the spreading of the infection from infected neighboring regions. We use a previously developed methodology and official municipality level data from the Portuguese Directorate-General for Health (DGS), relative to the first twelve months of the pandemic, to compute an estimate of the incidence rate in each location of mainland Portugal. The resulting sequence of incidence rate maps was then used as a gold standard to test the effectiveness of different approaches in the prediction of the spatial-temporal evolution of the incidence rate. Four different methods were tested: a simple cell level autoregressive moving average (ARMA) model, a cell level vector autoregressive (VAR) model, a municipality-by-municipality compartmental SIRD model followed by direct block sequential simulation and a convolutional sequence-to-sequence neural network model based on the STConvS2S architecture. We conclude that the convolutional sequence-to-sequence neural network is the best performing method, when predicting the medium-term future incidence rate, using the available information.