Scaling urban densities globally do not show economies of scale: Implications for contact rates

Abstract:

Urban Scaling Theory assumes contact rates increase allometrically with city size due to how population density scales with city size. However, empirical support for this assumption is limited. Here, we analyze two global compilations of urban population and area for hundreds of cities from ~ 20 countries. In both datasets, the majority of countries analyzed (18/22 DEM; 15/19 GHS) did not exhibit allometric scaling (slopes less than 1.0) but instead exhibited isometric scaling (slopes ~ 1.0) of population with area and thus constant densities across cities of varying sizes within countries. We find more variation in densities among countries (>1 order of magnitude) than within. Only a few (3/22) countries with high per capita income exhibit economies of scale (slopes significantly < 1), where larger cities become denser. We further illustrate the consequences of density scaling for contact rates with implications for human interactions leading to disease (e.g., SARS-CoV-2) and cultural transmission. Our results indicate that cities rarely exhibit economies of scale and therefore, epidemic dynamics are likely more influenced by socioeconomic factors and variation in mobility among countries rather than the scaling of city size. Because the scaling of human population density with city size strongly influences human social interactions, our results have implications for infrastructure, health, cultural evolution, social organization, governance, sustainability and questions key assumptions of heretofore Urban Scaling Theory. Specifically, it has implications for country-specific strategies for managing global pandemics.