COVID-19 is an ongoing public health emergency. Without a vaccine or effective antivirals, non-pharmaceutical interventions form the foundation of current response efforts. Quantifying the efficacy of these interventions is crucial. Using mortality data and a classification guide of state level responses, we relate the intensity of interventions to statistical estimates of transmission, finding that more stringent control measures are associated with larger reductions in disease proliferation. Additionally, we observe that transmission increases with population density, but not population size. These results may help inform future response efforts.

Apart from its global health importance, measles is a paradigm for low-dimensional mechanistic understanding of local nonlinear population interactions. A central question for spatio-temporal dynamics is the relative role of hierarchical spread from large cities to small towns and 'metapopulation' transmission among local small population clusters in measles persistence. Quantifying this balance is critical to planning regional elimination and global eradication of measles. Yet, current gravity models do not allow a formal comparison of hierarchical versus metapopulation spread. We address this gap with a competing-risks framework, capturing the relative importance of competing sources of reintroductions of infection. We apply the method to the uniquely spatio-temporally detailed urban incidence data set for measles in England and Wales (available in the Supporting Materials), from 1944 to the infection's vaccine-induced nadir in the 1990s. We find that despite the regional influence of a few large cities (e.g. London and Liverpool) metapopulation aggregation in neighboring towns and cities plays an important role in driving national dynamics in the prevaccination era. As vaccination levels increased in the 1970s and 80s, the signature of spatially predictable spread diminished: increasingly, infection was introduced from unidentifiable random sources possibly outside regional metapopulations. The resulting erratic dynamics highlight the challenges of identifying shifting sources of infection and characterizing patterns of incidence in times of high vaccination coverage. More broadly, the underlying incidence and demographic data, accompanying this paper, will also provide a significant resource for exploring nonlinear spatiotemporal population

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A key concern in public health is whether disparities exist between urban and rural areas. One dimension of potential variation is the transmission of infectious diseases. In addition to potential differences between urban and rural local dynamics, the question of whether urban and rural areas participate equally in national dynamics remains unanswered. Specifically, urban and rural areas may diverge in local transmission as well as spatial connectivity, and thus risk for receiving imported cases. Finally, the potential confounding relationship of spatial proximity with size and urban/rural district type has not been addressed by previous research. It is rare to have sufficient data to explore these questions thoroughly. We use exhaustive weekly case reports of measles in 954 urban and 468 rural districts of the UK (1944–1965) to compare both local disease dynamics as well as regional transmission. We employ the time-series susceptible–infected–recovered model to estimate disease transmission, epidemic severity, seasonality and import dependence. Congruent with past results, we observe a clear dependence on population size for the majority of these measures. We use a matched-pair strategy to compare proximate urban and rural districts and control for possible spatial confounders. This analytical strategy reveals a modest difference between urban and rural areas. Rural areas tend to be characterized by more frequent, smaller outbreaks compared to urban counterparts. The magnitude of the difference is slight and the results primarily reinforce the importance of population size, both in terms of local and regional transmission. In sum, urban and rural areas demonstrate remarkable epidemiological similarity in this recent UK context.