Impact of inter-city interactions on disease scaling.

Inter-city interactions are critical for the transmission of infectious diseases, yet their effects on the scaling of disease cases remain largely underexplored. Here, we use the commuting network as a proxy for inter-city interactions, integrating it with a general scaling framework to describe the incidence of seven infectious diseases across Brazilian cities as a function of population size and the number of commuters. Our models significantly outperform traditional urban scaling approaches, revealing that the relationship between disease cases and a combination of population and commuters varies across diseases and is influenced by both factors. Although most cities exhibit a less-than-proportional increase in disease cases with changes in population and commuters, more-than-proportional responses are also observed across all diseases. Notably, in some small and isolated cities, proportional rises in population and commuters correlate with a reduction in disease cases. These findings suggest that such towns may experience improved health outcomes and socioeconomic conditions as they grow and become more connected. However, as growth and connectivity continue, these gains diminish, eventually giving way to challenges typical of larger urban areas - such as socioeconomic inequality and overcrowding - that facilitate the spread of infectious diseases. Our study underscores the interconnected roles of population size and commuter dynamics in disease incidence while highlighting that changes in population size exert a greater influence on disease cases than variations in the number of commuters.