Abstract
Understanding human mobility is crucial for applications such as forecasting epidemic spreading, planning transport infrastructure and urbanism in general. While, traditionally, mobility information has been collected via surveys, the pervasive adoption of mobile technologies has brought a wealth of (real time) data. The easy access to this information opens the door to study theoretical questions so far unexplored. In this work, we show for a series of worldwide cities that commuting daily flows can be mapped into a well behaved vector field, fulfilling the divergence theorem and which is, besides, irrotational. This property allows us to define a potential for the field that can become a major instrument to determine separate mobility basins and discern contiguous urban areas. We also show that empirical fluxes and potentials can be well reproduced and analytically characterized using the so-called gravity model, while other models based on intervening opportunities have serious difficulties.
Highlights
Understanding human mobility is crucial for applications such as forecasting epidemic spreading, planning transport infrastructure and urbanism in general
Human mobility has been studied for decades due to the relevant role it plays in a wide spectrum of applications including economic questions and living conditions[1,2,3], city structure[4,5], forecasting epidemic spreading[6,7,8,9], traffic demand and design of new infrastructure[10], or urban pollution and air quality[11]
It is worth noticing that the quality of the OD matrices obtained from these new information and communication technologies (ICT) data sources have been confronted against the information provided by surveys with satisfactory results in urban areas at geographical scales larger than one square kilometer[18]
Summary
Understanding human mobility is crucial for applications such as forecasting epidemic spreading, planning transport infrastructure and urbanism in general. Two competing frameworks have been used for almost 80 years to characterize mobility flows: the gravity[22,23] and the intervening opportunity[24,25] models Their main difference lies in the way in which the geographical distance affects the flows. A few years ago, it has been introduced the so-called radiation model as an evolution of the intervening opportunity concept in which the opportunity selected is supposed to be the best possible choice simplifying the statistic treatment, and the density of opportunities is related to the population[30,31] This allows to write a closed formula for the probability of a trip to finish at a given geographical unit. After the gravity model introduction, the possibility of defining a potential was discussed[38] but the lack of reliable data prevented ulterior research in this direction
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