  Urban areas with larger and more connected populations offer an auspicious
environment for contagion processes such as the spread of pathogens. Empirical
evidence reveals a systematic increase in the rates of certain sexually
transmitted diseases (STDs) with larger urban population size. However, the
main drivers of these systemic infection patterns are still not well
understood, and rampant urbanization rates worldwide makes it critical to
advance our understanding on this front. Using confirmed-cases data for three
STDs in US metropolitan areas, we investigate the scaling patterns of
infectious disease incidence in urban areas. The most salient features of these
patterns are that, on average, the incidence of infectious diseases that
transmit with less ease-- either because of a lower inherent transmissibility
or due to a less suitable environment for transmission-- scale more steeply
with population size, are less predictable across time and more variable across
cities of similar size. These features are explained, first, using a simple
mathematical model of contagion, and then through the lens of a new theory of
urban scaling. These theoretical frameworks help us reveal the links between
the factors that determine the transmissibility of infectious diseases and the
properties of their scaling patterns across cities.
