First-wave COVID-19 daily cases obey gamma law

Modelling how a pandemic is spreading over time is a challenging issue. The new coronavirus disease called COVID-19 does not escape this rule as it has embraced over two hundred countries. As for previous pandemics, several studies have attempted to model the occurrence of cases caused by COVID-19. However, no study has succeeded in accurately modelling the impact of the infectious agent. Here we show that COVID-19 daily case distribution in humans obeys a Gamma law, which two new parameters can describe without any adjustment. Though the Gamma law has been exploited for nearly two centuries to describe the statistical distribution of spatial or temporal quantities, the goodness-of-fit rationale using two or three parameters has remained enigmatic. The new Gamma law approach we demonstrate here emerges from actual data and sheds light on the underlying mechanisms of the observed phenomenon. This finding has promising applicability in the epidemiological domain and in all disciplines involving branching systems, for which our Gamma law approach may bring a solution to hitherto unsolved problems.