  Epidemic data show the existence of a region of quasi-linear growth
(strolling period) of infected cases extending in between waves. We demonstrate
that this constitutes evidence for the existence of near time-scale invariance
that is neatly encoded via complex fixed points in the epidemic Renormalisation
Group approach. As a result we achieve a deeper understanding of multiple wave
dynamics and its inter-wave strolling regime. Our results are tested and
calibrated against the COVID-19 pandemic data. Because of the simplicity of our
approach that is organised around symmetry principles our discovery amounts to
a paradigm shift in the way epidemiological data are mathematically modelled.
