Three main mechanisms determining the dynamics of measles have been described in the literature: invasion in disease-free lands leading to import-dependent outbreaks, switching between annual and biennial attractors driven by seasonality, and amplification of stochastic fluctuations close to the endemic equilibrium. Here, we study the importance of the three mechanisms using a detailed geographical description of human mobility. We perform individual-based simulations of an SIR model using a gridded description of human settlements on top of which we implement human mobility according to the radiation model. Parallel computation permits detailed simulations of large areas. Focusing our research on the British Isles, we show that human mobility has an impact on the periodicity of measles outbreaks. Depending on the level of mobility, we observe at the global level multi-annual, annual or biennial cycles. The periodicity observed globally, however, differs from the local epidemic cycles: different locations show different mechanisms at work depending on both population size and mobility. As a result, the periodicities observed locally depend on the interplay between the local population size and human mobility.

We investigate the relationship between periodicity, synchronization and persistence of measles through simulations of geographical spread on the British Isles. We show that the establishment of areas of biennial periodicity depends on the interplay between human mobility and local population size and that locations undergoing biennial cycles tend to be, on average, synchronized in phase. We show however that occurrences of opposition of phase are actually quite common and correspond to stable dynamics. We also show that persistence is strictly related to circulation of the disease in the highly populated area of London and that this ensures survival of the disease even when human mobility drops to extremely low levels.

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