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

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.

Fractal signatures of the COVID-19 spread.

Recent quantitative approaches for studying several aspects of urban life and infrastructure have shown that scale properties allow the understanding of many features of urban infrastructure and of human activity in cities. In this paper, we show that COVID-19 virus contamination follows a similar pattern in different regions of the world. The superlinear power-law behavior for the number of contamination cases as a function of the city population, with exponent ß of the order of 1.15 is always obtained. Due to the strong indication that scaling is a determinant feature of covid-19 spread, we propose an epidemiological model that embodies a fractal structure, allowing a more detailed description of the observed data about the virus spread in different countries and regions. The hypothesis that fractal structures can be formed in cities as well as in larger networks is tested, indicating that indeed self-similarity may be found in networks connecting several cities.