Universal scaling law for COVID-19 propagation in urban centers

Cardoso, B.-H. F.; Goncalves, S.

Due to the COVID-19 pandemic, there is a high demand for Susceptible-Infective-Recovered (SIR) models to adjust and predict the number of cases in urban areas. Forecasting, however, is a difficult task, because the change in people's behavior reflects in a continuous change in the parameters of the model. An important question is what we can use from one city to another; if what happened in Madrid could have been applied to New York and then, if what we have learned from this city would be useful for Sao Paulo. To answer this question, we present an analysis of the transmission rate of COVID-19 as a function of population density and population size for US counties, cities of Brazil, German, and Portugal. Contrary to the common hypothesis in epidemics modeling, we observe a higher disease transmissibility for higher city's population density/size --with the latter showing more predicting power. We present a contact rate scaling theory that explain the results, predicting that the basic reproductive number $R_0$ of epidemics scales as the logarithm of the city size.