Introduced in its contemporary form in 1946 (ref. 1), but with roots that go back to the eighteenth century2, the gravity law1,3,4 is the prevailing framework with which to predict population movement3,5,6, cargo shipping volume7 and inter-city phone calls8,9, as well as bilateral trade flows between nations10. Despite its widespread use, it relies on adjustable parameters that vary from region to region and suffers from known analytic inconsistencies. Here we introduce a stochastic process capturing local mobility decisions that helps us analytically derive commuting and mobility fluxes that require as input only information on the population distribution. The resulting radiation model predicts mobility patterns in good agreement with mobility and transport patterns observed in a wide range of phenomena, from long-term migration patterns to communication volume between different regions. Given its parameter-free nature, the model can be applied in areas where we lack previous mobility measurements, significantly improving the predictive accuracy of most of the phenomena affected by mobility and transport processes11,12,13,14,15,16,17,18,19,20,21,22,23.
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We thank J. P. Bagrow, A. Fava, F. Giannotti, Y.-R. Lin, J. Menche, Z. Néda, D. Pedreschi, D. Wang, G. Wilkerson and D. Bauer for many discussions, and N. Ferguson for prompting us to look into the gravity law. A.M. and F.S. acknowledge the Cariparo foundation for financial support. This work was supported by the Network Science Collaborative Technology Alliance sponsored by the US Army Research Laboratory under Agreement Number W911NF-09-2-0053; the Office of Naval Research under Agreement Number N000141010968; the Defense Threat Reduction Agency awards WMD BRBAA07-J-2-0035 and BRBAA08-Per4-C-2-0033; and the James S. McDonnell Foundation 21st Century Initiative in Studying Complex Systems.
The authors declare no competing financial interests.
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Simini, F., González, M., Maritan, A. et al. A universal model for mobility and migration patterns. Nature 484, 96–100 (2012). https://doi.org/10.1038/nature10856
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