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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 the low-dimensional mechanistic understanding of local nonlinear population interactions. A central question for spatio-temporal dynamics is the relative roles 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 the 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 dataset for measles in England and Wales, from 1944 to the infection’s vaccine-induced nadir in the 1990s. We find that despite the regional influence of a few large cities (for example, London and Liverpool), metapopulation aggregation in neighbouring towns and cities played an important role in driving national dynamics in the prevaccination era. As vaccination levels increased in the 1970s and 1980s, 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 an important resource for exploring nonlinear spatiotemporal population dynamics.

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Fig. 1: A schematic illustration of the spatial dynamics and persistence of measles.
Fig. 2: Fit of the absence–presence–absence model in the competing-risks framework from 1944 to 1964.
Fig. 3: Prevaccination regional dynamics of measles, inferred from the absence–presence–absence model in a competing-risks framework.
Fig. 4: Impact of vaccination on the spatial spread of measles.

Data availability

The measles data are available at

Code availability

The code is available at


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We thank the RAPIDD Program of the US Department of Homeland Security and the Fogarty International Centre, National Institutes of Health (NIH). H.M.K. was also supported by the Eunice Kennedy Shriver National Institute of Child Health & Human Development of the NIH under award number P2CHD047879. A.D.B. was supported by a National Science Foundation Graduate Research Fellowship.

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Authors and Affiliations



M.S.Y.L. designed the research. M.S.Y.L., A.D.B. and B.T.G. performed the research. M.S.Y.L. analysed the data. M.S.Y.L., A.D.B., H.M.K., Q.C., D.J.S., C.J.E.M., O.N.B. and B.T.G. wrote the paper.

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Correspondence to Max S. Y. Lau.

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Supplementary Information

Supplementary Figs. 1 and 2, Tables 1 and 2, and Notes 1–3.

Reporting Summary

Spatiotemporal dynamics of measles in England and Wales 1944-1966

Pre-vaccination spatiotemporal dynamics of measles panning 1,451 urban and rural areas from 1944-1966. Dynamics remain strongly coupled throughout this era. Data are aggregated at the monthly scale, however weekly data are available within this manuscript.

Spatiotemporal dynamics of measles in England and Wales 1944-1994

Long-term spatiotemporal dynamics of measles panning 354 urban and rural areas from 1944 through to 1994. Dynamics are strongly coupled until the start of a mass measles-containing vaccination program in 1968, after which dynamics became de-coupled and erratic. Data are aggregated at the monthly scale, however weekly data are available within this manuscript.

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Lau, M.S.Y., Becker, A.D., Korevaar, H.M. et al. A competing-risks model explains hierarchical spatial coupling of measles epidemics en route to national elimination. Nat Ecol Evol 4, 934–939 (2020).

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