Scale-free dynamics of Covid-19 in a Brazilian city

Mathematical models can provide insights into the control of pandemic COVID-19, which remains a global priority. The dynamics of directly-transmitted infectious diseases, such as COVID-19, are usually described by compartmental models where individuals are classified as susceptible, infected and removed. These SIR models typically assume homogenous transmission of infection, even in large populations, a simplification that is convenient but inconsistent with observations. Here we use original data on the dynamics of COVID-19 spread in a Brazilian city to investigate the structure of the transmission network. We find that transmission can be described by a network in which each infectious individual has a small number of susceptible contacts, of the order of 2-5, which is independent of total population size. Compared with standard models of homogenous mixing, this scale-free, fractal infection process gives a better description of COVID-19 dynamics through time. In addition, the contact process explains the geographically localized clusters of disease seen in this Brazilian city. Our scale-free model can help refine criteria for physical and social distancing in order to more effectively mitigate the spread of COVID-19. We propose that scale-free COVID-19 dynamics could be a widespread phenomenon, a topic for further investigation.