Despite their importance for urban planning, traffic forecasting, and the spread of biological and mobile viruses, our understanding of the basic laws governing human motion remains limited thanks to the lack of tools to monitor the time resolved location of individuals. Here we study the trajectory of 100,000 anonymized mobile phone users whose position is tracked for a six month period. We find that in contrast with the random trajectories predicted by the prevailing Levy flight and random walk models, human trajectories show a high degree of temporal and spatial regularity, each individual being characterized by a time independent characteristic length scale and a significant probability to return to a few highly frequented locations. After correcting for differences in travel distances and the inherent anisotropy of each trajectory, the individual travel patterns collapse into a single spatial probability distribution, indicating that despite the diversity of their travel history, humans follow simple reproducible patterns. This inherent similarity in travel patterns could impact all phenomena driven by human mobility, from epidemic prevention to emergency response, urban planning and agent based modeling.
Uncovering the mechanism behind the scaling law in human trajectories is of fundamental significance in understanding many spatio-temporal phenomena. In combination of the exploration and the preferential returns, we propose a simple dynamical model mainly based on the cascading processes to capture the human mobility patterns. By the numerical simulations and analytical studies, we show more than five statistical characters that are well consistent with the empirical observations, including several type of scaling anomalies, and the ultraslow diffusion property, implying the cascading process…
This paper proposes a random walk model to analyze visitors' mobility patterns in a large museum. Visitors' available time makes their visiting styles different, resulting in dissimilarity in the order and number of visited places and in path sequence length. We analyze all this by comparing a simulation model and observed data, which provide us the strength of the visitors' mobility patterns. The obtained results indicate that shorter stay-type visitors exhibit stronger patterns than those with the longer stay-type, confirming that the former are more selective than the latter in terms of the…
It is highly believed that the individuals' mobility plays an important role in phase transition in animal collective motion. Here, we propose a model to study the effects of individuals' mobility in a distributed animal collective decision-making process, during which each individual faces two options with equal quality. We implement the quorum response rule, a type of social interaction rule which is taxonomically recognized in animal collective decision-making, as the sole interaction rule. After the introduction of individuals' mobility, we find that the group can reach a consensus decisio…
Despite the long history of modelling human mobility, we continue to lack a highly accurate approach with low data requirements for predicting mobility patterns in cities. Here, we present a population-weighted opportunities model without any adjustable parameters to capture the underlying driving force accounting for human mobility patterns at the city scale. We use various mobility data collected from a number of cities with different characteristics to demonstrate the predictive power of our model. We find that insofar as the spatial distribution of population is available, our model offers…
Data on vehicular mobility patterns have proved useful in many contexts. Yet generative models which accurately reproduce these mobility patterns are scarce. Here, we explore if recurrent neural networks can cure this scarcity. By training networks on taxi from NYC and Shanghai, and personal cars from Michigan, we show most aspects of the mobility patterns can be reproduced. In particular, the spatial distributions of the street segments usage is well captured by the recurrent neural networks, which other models struggle to do.
The availability of large-scale datasets collected via mobile phones has opened up opportunities to study human mobility at an individual level. The granular nature of these datasets calls for the design of summary statistics that can be used to describe succinctly mobility patterns. In this work, we show that the radius of gyration, a popular summary statistic to quantify the extent of an individual's whereabouts, suffers from a sensitivity to outliers, and is incapable of capturing mobility organised around multiple centres. We propose a natural generalisation of the radius of gyration to a …
University of Salzburg（萨尔茨堡大学）；CS Research Foundation（CS研究基金会）
We present and test a sequential learning algorithm for the short-term prediction of human mobility. This novel approach pairs the Exponential Weights forecaster with a very large ensemble of experts. The experts are individual sequence prediction algorithms constructed from the mobility traces of 10 million roaming mobile phone users in a European country. Average prediction accuracy is significantly higher than that of individual sequence prediction algorithms, namely constant order Markov models derived from the user's own data, that have been shown to achieve high accuracy in previous stud…
Introduced in its contemporary form by George Kingsley Zipf in 1946, but with roots that go back to the work of Gaspard Monge in the 18th century, the gravity law is the prevailing framework to predict population movement, cargo shipping volume, inter-city phone calls, as well as bilateral trade flows between nations. 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 fluxe…
Understanding the patterns of human mobility between cities has various applications from transport engineering to spatial modeling of the spreading of contagious diseases. We adopt a city-centric, data-driven perspective to quantify such patterns and introduce the mobility signature as a tool for understanding how a city (or a region) is embedded in the wider mobility network. We demonstrate the potential of the mobility signature approach through two applications that build on mobile-phone-based data from Finland. First, we use mobility signatures to show that the well-known radiation model …
From small steps to great leaps, metaphors of spatial mobility abound to describe discovery processes. Here, we ground these ideas in formal terms by systematically studying scientific knowledge mobility patterns. We use low-dimensional embedding techniques to create a knowledge space made up of 1.5 million articles from the fields of physics, computer science, and mathematics. By analyzing the publication histories of individual researchers, we discover patterns of knowledge mobility that closely resemble physical mobility. In aggregate, the trajectories form mobility flows that can be descri…
The non-pharmaceutical interventions (NPIs), aimed at reducing the diffusion of the COVID-19 pandemic, has dramatically influenced our behaviour in everyday life. In this work, we study how individuals adapted their daily movements and person-to-person contact patterns over time in response to the COVID-19 pandemic and the NPIs. We leverage longitudinal GPS mobility data of hundreds of thousands of anonymous individuals in four US states and empirically show the dramatic disruption in people's life. We find that local interventions did not just impact the number of visits to different venues b…
In this paper, we present a three-step methodological framework, including location identification, bias modification, and out-of-sample validation, so as to promote human mobility analysis with social media data. More specifically, we propose ways of identifying personal activity-specific places and commuting patterns in Beijing, China, based on Weibo (China's Twitter) check-in records, as well as modifying sample bias of check-in data with population synthesis technique. An independent citywide travel logistic survey is used as the benchmark for validating the results. Obvious differences ar…
Mobile phone data has enabled the timely and fine-grained study human mobility. Call Detail Records, generated at call events, allow building descriptions of mobility at different resolutions and with different spatial, temporal and social granularity. Individual trajectories are the basis for long-term observation of mobility patterns and identify factors of human dynamics. Here we propose a systematic analysis to characterize mobility network flows and topology and assess their impact into individual traces. Discrete flow-based descriptors are used to classify and understand human mobility p…
In the advent of a pervasive presence of location sharing services researchers gained an unprecedented access to the direct records of human activity in space and time. This paper analyses geo-located Twitter messages in order to uncover global patterns of human mobility. Based on a dataset of almost a billion tweets recorded in 2012 we estimate volumes of international travelers in respect to their country of residence. We examine mobility profiles of different nations looking at the characteristics such as mobility rate, radius of gyration, diversity of destinations and a balance of the infl…
The study of human mobility patterns is of both theoretical and practical values in many aspects. For long-distance travels, a few research endeavors have shown that the displacements of human travels follow the power-law distribution. However, controversies remain in the issue of the scaling law of human mobility in intra-urban areas. In this work we focus on the mobility pattern of taxi passengers by examining five datasets of the three metropolitans of New York, Dalian and Nanjing. Through statistical analysis, we find that the lognormal distribution with a power-law tail can best approxima…
Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations and recurrent flows and poorly modeled by the random diffusive dynamics generally used to study them. Here we develop a theoretical framework to analyze contagion within a network of locations where individuals recall their geographic origins. We find a phase transition between a regime in which the contagion affects a large fraction of the system and one in w…
The analysis of longitudinal travel data enables investigating how mobility patterns vary across the population and identify the spatial properties thereof. The objective of this study is to identify the extent to which users explore different parts of the network as well as identify distinctive user groups in terms of the spatial extent of their mobility patterns. To this end, we propose two means for representing spatial mobility profiles and clustering travellers accordingly. We represent users patterns in terms of zonal visiting frequency profiles and grid-cells spatial extent heatmaps. We…
Crime has been previously explained by social characteristics of the residential population and, as stipulated by crime pattern theory, might also be linked to human movements of non-residential visitors. Yet a full empirical validation of the latter is lacking. The prime reason is that prior studies are limited to aggregated statistics of human visitors rather than mobility flows and, because of that, neglect the temporal dynamics of individual human movements. As a remedy, we provide the first work which studies the ability of granular human mobility in describing and predicting crime concen…
SARS-CoV-2 emerged in late 2019. Since then, it has spread to several countries, becoming classified as a pandemic. So far, there is no definitive treatment or vaccine, so the best solution is to prevent transmission between individuals through social distancing. However, it is difficult to measure the effectiveness of these distance measures. Therefore, this study uses data from Google COVID-19 Community Mobility Reports to try to understand the mobility patterns of the Portuguese population during the COVID-19 pandemic. In this study, the Rt value was modeled for Portugal. Also, the changepo…
Human mobility is an important characteristic of human behavior, but since tracking personalized position to high temporal and spatial resolution is difficult, most studies on human mobility patterns rely largely on mathematical models. Seminal models which assume frequently visited locations tend to be re-visited, reproduce a wide range of statistical features including collective mobility fluxes and numerous scaling laws. However, these models cannot be verified at a time-scale relevant to our daily travel patterns as most available data do not provide the necessary temporal resolution. In t…
Understanding human mobility from a microscopic point of view may represent a fundamental breakthrough for the development of a statistical physics for cognitive systems and it can shed light on the applicability of macroscopic statistical laws for social systems. Even if the complexity of individual behaviors prevents a true microscopic approach, the introduction of mesoscopic models allows the study of the dynamical properties for the non-stationary states of the considered system. We propose to compute various entropy measures of the individual mobility patterns obtained from GPS data that …
The study of human mobility patterns is a crucially important research field for its impact on several socio-economic aspects and, in particular, the measure of regularity patters of human mobility can provide a across-the-board view of many social distancing variables in epidemics such as: human movement trends, physical interpersonal distances and population density. We will show that the notion of information entropy is also strongly related to demographic and economic trends by the use and analysis of real-time data. In the present research paper we address three different problems. First,…
The analysis of contagion-diffusion processes in metapopulations is a powerful theoretical tool to study how mobility influences the spread of communicable diseases. Nevertheless, many metapopulation approaches use indistinguishable agents to alleviate analytical difficulties. Here, we address the impact that recurrent mobility patterns, and the spatial distribution of distinguishable agents, have on the unfolding of epidemics in large urban areas. We incorporate the distinguishable nature of agents regarding both, their residence, and their usual destination. The proposed model allows both a …
While the fat tailed jump size and the waiting time distributions characterizing individual human trajectories strongly suggest the relevance of the continuous time random walk (CTRW) models of human mobility, no one seriously believes that human traces are truly random. Given the importance of human mobility, from epidemic modeling to traffic prediction and urban planning, we need quantitative models that can account for the statistical characteristics of individual human trajectories. Here we use empirical data on human mobility, captured by mobile phone traces, to show that the predictions …
This research evidences the usefulness of open big data to map mobility patterns in a medium-sized city. Motivated by the novel analysis that big data allow worldwide and in large metropolitan areas, we developed a methodology aiming to complement origin-destination surveys with à la carte spatial boundaries and updated data at a minimum cost. This paper validates the use of Twitter data to map the impact of public spaces on the different parts of the metropolitan area of Concepción, Chile. Results have been validated by local experts and evidence the main mobility patterns towards spaces of s…
Human mobility plays a key role on the transformation of local disease outbreaks into global pandemics. Thus, the inclusion of human movements into epidemic models has become mandatory for understanding current epidemic episodes and to design efficient prevention policies. Following this challenge, here we develop a Markovian framework which enables to address the impact of recurrent mobility patterns on the epidemic onset at different temporal scales. This formalism is validated by comparing their predictions with results from mechanistic simulations. The fair agreement between both theory an…
Recently, many empirical studies uncovered that animal foraging, migration and human traveling obey Levy flights with an exponent around -2. Inspired by the deluge of H1N1 this year, in this paper, the effects of Levy flights' mobility pattern on epidemic spreading is studied from a network perspective. We construct a spatial weighted network which possesses Levy flight spatial property under a restriction of total energy. The energy restriction is represented by the limitation of total travel distance within a certain time period of an individual. We find that the exponent -2 is the epidemic …
Gyration radius of individual's trajectory plays a key role in quantifying human mobility patterns. Of particular interests, empirical analyses suggest that the growth of gyration radius is slow versus time except the very early stage and may eventually arrive to a steady value. However, up to now, the underlying mechanism leading to such a possibly steady value has not been well understood. In this Letter, we propose a simplified human mobility model to simulate individual's daily travel with three sequential activities: commuting to workplace, going to do leisure activities and returning hom…
Public stakeholders implement several policies and regulations to tackle gender gaps, fostering the change in the cultural constructs associated with gender. One way to quantify if such changes elicit gender equality is by studying mobility. In this work, we study the daily mobility patterns of women and men occurring in Medellín (Colombia) in two years: 2005 and 2017. Specifically, we focus on the spatiotemporal differences in the travels and find that purpose of travel and occupation characterise each gender differently. We show that women tend to make shorter trips, corroborating Ravenstein…
The implementation of social distancing policies is key to reducing the impact of the current COVID-19 pandemic. However, their effectiveness ultimately depends on human behavior. In the United States, compliance with social distancing policies has widely varied thus far during the pandemic. But what drives such variability? Through six open datasets, including actual human mobility, we estimated the association between mobility and the growth rate of COVID-19 cases across 3,107 U.S. counties, generalizing previous reports. In addition, data from the 2016 U.S. presidential election was used to…
Data on human spatial distribution and movement is essential for understanding and analyzing social systems. However existing sources for this data are lacking in various ways; difficult to access, biased, have poor geographical or temporal resolution, or are significantly delayed. In this paper, we describe how geolocation data from Twitter can be used to estimate global mobility patterns and address these shortcomings. These findings will inform how this novel data source can be harnessed to address humanitarian and development efforts.
Getting insights on human mobility patterns and being able to reproduce them accurately is of the utmost importance in a wide range of applications from public health, to transport and urban planning. Still the relationship between the effort individuals will invest in a trip and its purpose importance is not taken into account in the individual mobility models that can be found in the recent literature. Here, we address this issue by introducing a model hypothesizing a relation between the importance of a trip and the distance traveled. In most practical cases, quantifying such importance is …
Characterizing the movement patterns of animals is crucial to improve our understanding of their behavior and thus develop adequate conservation strategies. Such investigations, which could not have been implemented in practice only a few years ago, have been facilitated through the recent advances in tracking methods that enable researchers to study animal movement at an unprecedented spatio-temporal resolution. However, the identification and extraction of patterns from spatio-temporal trajectories is still a general problem that has relevance for many applications. Here, we rely on the conc…
As a highly infectious respiratory disease, COVID-19 has become a pandemic that threatens global health. Without an effective treatment, non-pharmaceutical interventions, such as travel restrictions, have been widely promoted to mitigate the outbreak. Current studies analyze mobility metrics such as travel distance; however, there is a lack of research on interzonal travel flow and its impact on the pandemic. Our study specifically focuses on the inter-county mobility pattern and its influence on the COVID-19 spread in the United States. To retrieve real-world mobility patterns, we utilize an …
Recent seminal works on human mobility have shown that individuals constantly exploit a small set of repeatedly visited locations. A concurrent literature has emphasized the explorative nature of human behavior, showing that the number of visited places grows steadily over time. How to reconcile these seemingly contradicting facts remains an open question. Here, we analyze high-resolution multi-year traces of $\sim$40,000 individuals from 4 datasets and show that this tension vanishes when the long-term evolution of mobility patterns is considered. We reveal that mobility patterns evolve signi…
By using an appropriate version of the synchronous SIR model, we studied the effects of dilution and mobility on the critical immunization rate. We showed that, by applying time-dependent Monte Carlo (MC) simulations at criticality, and taking into account the optimization of the power law for the density of infected individuals, the critical immunization necessary to block the epidemic in two-dimensional lattices decreases as dilution increases with a logarithmic dependence. On the other hand, the mobility minimizes such effects and the critical immunizations is greater when the probability o…
Understanding the patterns of mobility of individuals is crucial for a number of reasons, from city planning to disaster management. There are two common ways of quantifying the amount of travel between locations: by direct observations that often involve privacy issues, e.g., tracking mobile phone locations, or by estimations from models. Typically, such models build on accurate knowledge of the population size at each location. However, when this information is not readily available, their applicability is rather limited. As mobile phones are ubiquitous, our aim is to investigate if mobility…
Metapopulation models have been a powerful tool for both theorizing and simulating epidemic dynamics. In a metapopulation model, one considers a network composed of subpopulations and their pairwise connections, and individuals are assumed to migrate from one subpopulation to another obeying a given mobility rule. While how different mobility rules affect epidemic dynamics in metapopulation models has been studied, there have been relatively few efforts on comparison of the effects of simple (i.e., unbiased) random walks and more complex mobility rules. Here we study a susceptible-infectious-s…
The objective of this study is to propose and test an adaptive reinforcement learning model that can learn the patterns of human mobility in a normal context and simulate the mobility during perturbations caused by crises, such as flooding, wildfire, and hurricanes. Understanding and predicting human mobility patterns, such as destination and trajectory selection, can inform emerging congestion and road closures raised by disruptions in emergencies. Data related to human movement trajectories are scarce, especially in the context of emergencies, which places a limitation on applications of exi…
Human mobility is subject to collective dynamics that are the outcome of numerous individual choices. Smart card data which originated as a means of facilitating automated fare collections has emerged as an invaluable source for analyzing human mobility patterns. A variety of clustering and segmentation techniques has been adopted and adapted for applications ranging from passenger demand market segmentation to the analysis of urban activity locations. In this paper we provide a systematic review of the state-of-the-art on clustering public transport users based on their temporal or spatial-te…
We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of the model on regular and complex metapopulation network topologies and show that significant dynamical differences exist to ordinary reaction-diffusion and effective force of infection models. On a lattice we calculate an expression for the velocity of the propagating epidemic front and find that in contrast to the diffusive systems, our model predicts a satu…
The spreading of epidemics is very much determined by the structure of the contact network, which may be impacted by the mobility dynamics of the individuals themselves. In confined scenarios where a small, closed population spends most of its time in localized environments and has easily identifiable mobility patterns --such as workplaces, university campuses or schools-- it is of critical importance to identify the factors controlling the rate of disease spread. Here we present a discrete-time, metapopulation-based model to describe the transmission of SIS-like diseases that take place in co…
The individual movements of large numbers of people are important in many contexts, from urban planning to disease spreading. Datasets that capture human mobility are now available and many interesting features have been discovered, including the ultra-slow spatial growth of individual mobility. However, the detailed substructures and spatiotemporal flows of mobility - the sets and sequences of visited locations - have not been well studied. We show that individual mobility is dominated by small groups of frequently visited, dynamically close locations, forming primary "habitats" capturing typ…
Human mobility, contact patterns, and their interplay are key aspects of our social behavior that shape the spread of infectious diseases across different regions. In the light of new evidence and data sets about these two elements, epidemic models should be refined to incorporate both the heterogeneity of human contacts and the complexity of mobility patterns. Here, we propose a theoretical framework that allows accommodating these two aspects in the form of a set of Markovian equations. We validate these equations with extensive mechanistic simulations and derive analytically the epidemic th…
Social structures influence a variety of human behaviors including mobility patterns, but the extent to which one individual's movements can predict another's remains an open question. Further, latent information about an individual's mobility can be present in the mobility patterns of both social and non-social ties, a distinction that has not yet been addressed. Here we develop a "colocation" network to distinguish the mobility patterns of an ego's social ties from those of non-social colocators, individuals not socially connected to the ego but who nevertheless arrive at a location at the s…
A range of early studies have been conducted to illustrate human mobility patterns using different tracking data, such as dollar notes, cell phones and taxicabs. Here, we explore human mobility patterns based on massive tracking data of US flights. Both topological and geometric properties are examined in detail. We found that topological properties, such as traffic volume (between airports) and degree of connectivity (of individual airports), including both in- and outdegrees, follow a power law distribution but not a geometric property like travel lengths. The travel lengths exhibit an expon…
By means of the asynchronous cellular automata algorithm we study stationary states and spatial patterning in an $SIS$ model, in which the individuals' are attached to the vertices of a graph and their mobility is mimicked by varying the neighbourhood size $q$. The versions with fixed $q$ and those taken at random at each step and for each individual are studied. Numerical data on the local behaviour of the model are mapped onto the solution of its zero dimensional version, corresponding to the limit $q\to +\infty$ and equivalent to the logistic growth model. This allows for deducing an explic…
We develop a multiple-events model and exploit within and between country variation in the timing, type and level of intensity of various public policies to study their dynamic effects on the daily incidence of COVID-19 and on population mobility patterns across 135 countries. We remove concurrent policy bias by taking into account the contemporaneous presence of multiple interventions. The main result of the paper is that cancelling public events and imposing restrictions on private gatherings followed by school closures have quantitatively the most pronounced effects on reducing the daily in…
