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.

Assessing the impact of mobility on epidemic spreading is of crucial importance for understanding the effect of policies like mass quarantines and selective re-openings. High mobility between areas contribute to the importation of cases, affecting the spread of the disease. While many factors influence local incidence and making it more or less homogeneous with respect to other areas, the importance of multi-seeding has often been overlooked. Multi-seeding occurs when several independent (non-clustered) infected individuals arrive at a susceptible population. This can give rise to autonomous outbreaks that impact separate areas of the contact (social) network. Such mechanism has the potential to boost local incidence and size, making control and tracing measures less effective. In Spain, the high heterogeneity in incidence between similar areas despite the uniform mobility control measures taken suggests that multi-seeding could have played an important role in shaping the spreading of the disease. In this work, we focus on the spreading of SARS-CoV-2 among the 52 Spanish provinces, showing that local peaks of incidence and mortality strongly correlate with mobility occurred in the early-stage weeks from and to Madrid, the main mobility hub and where the initial local outbreak unfolded. These results clarify the higher order effects that mobility can have on the evolution of an epidemic and highlight the relevance of its control.

Monitoring migration flows is crucial to respond to humanitarian crisis and to design efficient policies. This information usually comes from surveys and border controls, but timely accessibility and methodological concerns reduce its usefulness. Here, we propose a method to detect migration flows worldwide using geolocated Twitter data. We focus on the migration crisis in Venezuela and show that the calculated flows are consistent with official statistics at country level. Our method is versatile and far-reaching, as it can be used to study different features of migration as preferred routes, settlement areas, mobility through several countries, spatial integration in cities, etc. It provides finer geographical and temporal resolutions, allowing the exploration of issues not contemplated in official records. It is our hope that these new sources of information can complement official ones, helping authorities and humanitarian organizations to better assess when and where to intervene on the ground.

Interactions between people are the basis on which the structure of our society arises as a complex system and, at the same time, are the starting point of any physical description of it. In the last few years, much theoretical research has addressed this issue by combining the physics of complex networks with a description of interactions in terms of evolutionary game theory. We here take this research a step further by introducing a most salient societal factor such as the individuals' preferences, a characteristic that is key to understand much of the social phenomenology these days. We consider a heterogeneous, agent-based model in which agents interact strategically with their neighbors but their preferences and payoffs for the possible actions differ. We study how such a heterogeneous network behaves under evolutionary dynamics and different strategic interactions, namely coordination games and best shot games. With this model we study the emergence of the equilibria predicted analytically in random graphs under best response dynamics, and we extend this test to unexplored contexts like proportional imitation and scale free networks. We show that some theoretically predicted equilibria do not arise in simulations with incomplete Information, and we demonstrate the importance of the graph topology and the payoff function parameters for some games. Finally, we discuss our results with available experimental evidence on coordination games, showing that our model agrees better with the experiment that standard economic theories, and draw hints as to how to maximize social efficiency in situations of conflicting preferences.

Assessing the impact of mobility on epidemic spreading is of crucial importance for understanding the effect of policies like mass quarantines and selective re-openings. While many factors affect disease incidence at a local level, making it more or less homogeneous with respect to other areas, the importance of multi-seeding has often been overlooked. Multi-seeding occurs when several independent (non-clustered) infected individuals arrive at a susceptible population. This can lead to independent outbreaks that spark from distinct areas of the local contact (social) network. Such mechanism has the potential to boost incidence, making control efforts and contact tracing less effective. Here, through a modeling approach we show that the effect produced by the number of initial infections is non-linear on the incidence peak and peak time. When case importations are carried by mobility from an already infected area, this effect is further enhanced by the local demography and underlying mixing patterns: the impact of every seed is larger in smaller populations. Finally, both in the model simulations and the analysis, we show that a multi-seeding effect combined with mobility restrictions can explain the observed spatial heterogeneities in the first wave of COVID-19 incidence and mortality in five European countries. Our results allow us for identifying what we have called epidemic epicenter: an area that shapes incidence and mortality peaks in the entire country. The present work further clarifies the nonlinear effects that mobility can have on the evolution of an epidemic and highlight their relevance for epidemic control.