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.

中文翻译：

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竞争风险模型解释了麻疹流行病在全国消灭过程中的等级空间耦合。

除了对全球健康的重要性外，麻疹是对局部非线性人群相互作用的低维机械理解的范例。时空动态的一个核心问题是等级从大城市到小城镇的相对作用以及在麻疹持续存在的地方小人群之间的种群传播。量化这种平衡对于规划区域消灭麻疹和全球消灭麻疹至关重要。但是，当前的引力模型不允许形式比较和人口分布的正式比较。我们通过竞争风险框架解决了这一差距，抓住了感染重新引入的竞争来源的相对重要性。我们将该方法应用于英格兰和威尔士的麻疹唯一时空详细的城市发病率数据集，从1944年到1990年代感染疫苗的最低点。我们发现，尽管一些大城市（例如伦敦和利物浦）具有区域影响力，但邻近城镇的人口聚集在预防接种前时代在推动国家动态方面发挥了重要作用。在1970年代和1980年代，随着疫苗接种水平的提高，在空间上可预测的传播特征减弱了：越来越多地，感染是由可能来自区域性人群之外的随机来源引入的。由此产生的不稳定现象突出表明了在高疫苗接种覆盖率时识别不断变化的感染源和表征发病模式的挑战。更广泛地说，本文随附的潜在发病率和人口统计数据