Evidence for Complex Fixed Points in Pandemic Data

Abstract

Mathematical models used in epidemiology to describe the diffusion of infectious diseases often fail to reproduce the recurrent appearance of exponential growth in the number of infections (waves). This feature requires a time-modulation of some parameters of the model. Moreover, 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 Renormalization Group approach. As a result, we obtain the first consistent mathematical description 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 organized around symmetry principles, our discovery amounts to a paradigm shift in the way epidemiological data are mathematically modelled. We show that the strolling period is crucial in controlling the emergence of the next wave, thus encouraging the maintenance of (non)pharmaceutical measures during the period following a wave.