  When it came to Covid-19, timing was everything. This paper considers the
spatiotemporal dynamics of the Covid-19 pandemic via a developed methodology of
non-Euclidean spatially aware functional registration. In particular, the daily
SARS-CoV-2 incidence in each of 380 local authorities in the UK from March to
June 2020 is analysed to understand the phase variation of the waves when
considered as curves. This is achieved by adapting a traditional registration
method (that of local variation analysis) to account for the clear spatial
dependencies in the data. This adapted methodology is shown via simulation
studies to perform substantially better for the estimation of the registration
functions than the non-spatial alternative. Moreover, it is found that the
driving time between locations represents the spatial dependency in the
Covid-19 data better than geographical distance. However, since driving time is
non-Euclidean, the traditional spatial frameworks break down; to solve this, a
methodology inspired by multidimensional scaling is developed to approximate
the driving times by a Euclidean distance which enables the established theory
to be applied. Finally, the resulting estimates of the registration/warping
processes are analysed by taking functionals to understand the qualitatively
observable earliness/lateness and sharpness/flatness of the Covid-19 waves
quantitatively.
