We analyse and mutually compare time series of COVID-19-related data and mobility data across Belgium's 43 arrondissements (NUTS 3). In this way, we reach three conclusions. First, we could detect a decrease in mobility during high-incidence stages of the pandemic. This is expressed as a significant change in the average amount of time spent outside one's home arrondissement, investigated over five distinct periods, and in more detail using an inter-arrondissement ``connectivity index'' (CI). Second, we analyse spatio-temporal COVID-19-related hospitalisation time series, after smoothing them using a generalise additive mixed model (GAMM). We confirm that some arrondissements are ahead of others and morphologically dissimilar to others, in terms of epidemiological progression. The tools used to quantify this are time-lagged cross-correlation (TLCC) and dynamic time warping (DTW), respectively. Third, we demonstrate that an arrondissement's CI with one of the three identified first-outbreak arrondissements is ... : Main text: 17 pages, 11 figures. Appendices: 4 pages, 4 figures. References: 44 ...