Tobler’s law and wavefront patterns in the spatial spread of COVID-19 across Europe during the Delta and Omicron waves

Aims: Epidemic wavefront models predict the spread of medieval pandemics such as the plague well. Our aim was to explore whether they contribute to understanding the spread of COVID-19, the first truly global pandemic of the 21st century with its fast and frequent international travel links. Methods: We analysed the spatial spread of reaching a threshold of very high incidence of new daily infections of the virus across European countries in the autumn of 2021 in which the Delta variant was dominant, as well as an even higher threshold of incidence in the subsequent spread of infections across the same set of countries during the winter of 2021/2022 when the Omicron variant of the virus became dominant. Results: We found patterns that are consistent with wavefront models for both periods of the pandemic in Europe. Conclusions: Modern means of transportation strongly accelerated the spread of the virus and typically generated diffusion patterns along bidirectional constrained mobility networks in addition to stochastic diffusion processes. However, since the majority of mobility, including mobility across international borders, is over short distances, wavefront patterns in the spread of a pandemic are still to be expected.