Mathematical Modeling of Spatio-Temporal Disease Spreading Using PDEs for Machine Learning

Abstract

In this paper, we numerically solve a foundational PDE that describes the spatio-temporal spread of an infectious disease. We solve this PDE with various different epidemiological parameters on the domain of Germany and map the solutions onto geographical regions. This solution, in combination with geographical distances and adjacencies, serves as a dataset to train and validate various machine learning models on the task of epidemiological predictions. We evaluate the abilities of prominent models on this dataset to forecast the spatio-temporal spread of a simulated infectious disease, their robustness, and denoising capabilities. This evaluation undermines the importance of testing performance and robustness separately.