A competing risks model explains hierarchical spatial coupling of measles epidemics en route to national elimination

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 dynamics.