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

•We present a new model based on the fractal structure of social groups to describe the epidemic spread of diseases.•The model gives the number of contacts among those individuals infecting the population.•The q-exponential function is the basic mathematical tool to describe the transmission of the virus.•The SIR model is a special case of the fractal model, recovered when the number of contacts is sufficiently large.•We demonstrated the model’s self-consistency. The model reproduces the data more accurately than the SIR model. A common basis to address the dynamics of directly transmitted infectious diseases, such as COVID-19, are compartmental (or SIR) models. SIR models typically assume homogenous population mixing, a simplification that is convenient but unrealistic. Here we validate an existing model of a scale-free fractal infection process using high-resolution data on COVID-19 spread in São Caetano, Brazil. 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. This model parameter correlated tightly with physical distancing measured by mobile phone data, such that in periods of greater distancing the model recovered a lower average number of contacts, and vice versa. We show that the SIR model is a special case of our scale-free fractal process model in which the parameter that reflects population structure is set at unity, indicating homogeneous mixing. Our more general framework better explained the dynamics of COVID-19 in São Caetano, used fewer parameters than a standard SIR model and accounted for geographically localized clusters of disease. Our model requires further validation in other locations and with other directly transmitted infectious agents.