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Pandemics, like the 1918 Spanish Influenza and COVID-19, spread throughregions of the World in subsequent waves. There is, however, no consensus onthe origin of this pattern, which may originate from human behaviour ratherthan from the virus diffusion itself. Time-honoured models of the SIR type orothers based on complex networks describe well the exponential spread of thedisease, but cannot naturally accommodate the wave pattern. Nevertheless,understanding this time-structure is of paramount importance in designingeffective prevention measures. Here we propose a consistent picture of the wavepattern based on the epidemic Renormalisation Group (eRG) framework, which isguided by the global symmetries of the system under time rescaling. We showthat the rate of spreading of the disease can be interpreted as a time-dilationsymmetry, while the final stage of an epidemic episode corresponds to reachinga time scale-invariant state. We find that the endemic period between two wavesis a sign of instability in the system, associated to near-breaking of the timescale-invariance. This phenomenon can be described in terms of an eRG modelfeaturing complex fixed points. Our results demonstrate that the key to controlthe arrival of the next wave of a pandemic is in the strolling period inbetween waves, i.e. when the number of infections grow linearly. Thus, limitingthe virus diffusion in this period is the most effective way to prevent ordelay the arrival of the next wave. In this work we establish a new guidingprinciple for the formulation of mid-term governmental strategies to curbpandemics and avoid recurrent waves of infections, deleterious in terms ofhuman life loss and economic damage.

Multiwave pandemic dynamics explained: How to tame the next wave of infectious diseases