COVID-19: $R_0$ is lower where outbreak is larger

Highlights

• We analyze COVID-19 diffusion in Italian municipalities with the same health system.

• Correlation between prevalence and rate of diffusion is negative, strong, and robust.

• This represents novel cross-sectional evidence of the prevalence-response elasticity.

• Based on epidemiological data, we rule out herd immunity and alternative explanations.

• Publication of accurate epidemiological data hence contributes to reducing contagion.

Abstract

We use daily data from Lombardy, the Italian region most affected by the COVID-19 outbreak, to calibrate a SIR model on each municipality. Municipalities with a higher initial number of cases feature a lower rate of diffusion, not attributable to herd immunity: there is a robust and strongly significant negative correlation between the estimated basic reproduction number ($R_0$) and the initial outbreak size. This represents novel evidence of the prevalence-response elasticity in a cross-sectional setting, characterized by a same health system and homogeneous social distancing regulations. By ruling out alternative explanations, we conclude that a higher number of cases causes changes of behavior, such as a more strict adoption of social distancing measures among the population, that reduce the spread. This finding calls for the distribution of detailed epidemiological data to populations affected by COVID-19 outbreaks.