A Generalized Radiation Model for Human Mobility: Spatial Scale, Searching Direction and Trip Constraint

Spatial Interaction Analysis of Infectious Disease Import and Export between Regions

Human travel plays a crucial role in the spread of infectious disease between regions. Travel of infected individuals from one region to another can transport a virus to places that were previously unaffected or may accelerate the spread of disease in places where the disease is not yet well established. We develop and apply models and metrics to analyze the role of inter-regional travel relative to the spread of disease, drawing from data on COVID-19 in the United States. To better understand how transportation affects disease transmission, we established a multi-regional time-varying compartmental disease model with spatial interaction. The compartmental model was integrated with statistical estimates of travel between regions. From the integrated model, we derived a transmission import index to assess the risk of COVID-19 transmission between states. Based on the index, we determined states with high risk for disease spreading to other states at the scale of months, and we analyzed how the index changed over time during 2020. Our model provides a tool for policymakers to evaluate the influence of travel between regions on disease transmission in support of strategies for epidemic control.

Radiation model for migration with directional preferences

The radiation model is a parameter-free model of human mobility that has been applied primarily for short-distance moves, such as commuting. When applied to migration, it underestimates the number of long-range moves, such as between different US states. Here we show that it additionally suffers from a conceptual inconsistency that can have substantial numerical effects on long-distance moves. We propose a modification of the radiation model that introduces a dependence on the angle between any two alternative potential destinations, accounting for the possibility that migrants may have preferences about the approximate direction of their move. We demonstrate that this modification mitigates the conceptual inconsistency and improves the model fit to observational migration data, without introducing any fitting parameters.

Modeling international mobility using roaming cell phone traces during COVID-19 pandemic

Most of the studies related to human mobility are focused on intra-country mobility. However, there are many scenarios (e.g., spreading diseases, migration) in which timely data on international commuters are vital. Mobile phones represent a unique opportunity to monitor international mobility flows in a timely manner and with proper spatial aggregation. This work proposes using roaming data generated by mobile phones to model incoming and outgoing international mobility. We use the gravity and radiation models to capture mobility flows before and during the introduction of non-pharmaceutical interventions. However, traditional models have some limitations: for instance, mobility restrictions are not explicitly captured and may play a crucial role. To overtake such limitations, we propose the COVID Gravity Model (CGM), namely an extension of the traditional gravity model that is tailored for the pandemic scenario. This proposed approach overtakes, in terms of accuracy, the traditional models by 126.9% for incoming mobility and by 63.9% when modeling outgoing mobility flows.

Generalized radiation model for human migration

One of the main problems in the study of human migration is predicting how many people will migrate from one place to another. An important model used for this problem is the radiation model for human migration, which models locations as attractors whose attractiveness is moderated by distance as well as attractiveness of neighboring locations. In the model, the measure used for attractiveness is population which is a proxy for economic opportunities and jobs. However, this may not be valid, for example, in developing countries, and fails to take into account people migrating for non-economic reasons such as quality of life. Here, we extend the radiation model to include the number of amenities (offices, schools, leisure places, etc.) as features aside from population. We find that the generalized radiation model outperforms the radiation model by as much as 10.3% relative improvement in mean absolute percentage error based on actual census data five years apart. The best performing model does not even include population information which suggests that amenities already include the information that we get from population. The generalized radiation model provides a measure of feature importance thus presenting another avenue for investigating the effect of amenities on human migration.

Comparative Analysis of Geolocation Information through Mobile-Devices under Different COVID-19 Mobility Restriction Patterns in Spain

The COVID-19 pandemic is changing the world in unprecedented and unpredictable ways. Human mobility, being the greatest facilitator for the spread of the virus, is at the epicenter of this change. In order to study mobility under COVID-19, to evaluate the efficiency of mobility restriction policies, and to facilitate a better response to future crisis, we need to understand all possible mobility data sources at our disposal. Our work studies private mobility sources, gathered from mobile-phones and released by large technological companies. These data are of special interest because, unlike most public sources, it is focused on individuals rather than on transportation means. Furthermore, the sample of society they cover is large and representative. On the other hand, these data are not directly accessible for anonymity reasons. Thus, properly interpreting its patterns demands caution. Aware of that, we explore the behavior and inter-relations of private sources of mobility data in the context of Spain. This country represents a good experimental setting due to both its large and fast pandemic peak and its implementation of a sustained, generalized lockdown. Our work illustrates how a direct and naive comparison between sources can be misleading, as certain days (e.g., Sundays) exhibit a directly adverse behavior. After understanding their particularities, we find them to be partially correlated and, what is more important, complementary under a proper interpretation. Finally, we confirm that mobile-data can be used to evaluate the efficiency of implemented policies, detect changes in mobility trends, and provide insights into what new normality means in Spain.

Kernel-based formulation of intervening opportunities for spatial interaction modelling

Understanding spatial interactions such as human mobility has been one of the main analytical themes in geography, spatial economics, and traffic engineering for a long time. The intervening opportunities models, including the radiation model, provide a framework to elucidate spatial interactions generated by an individual's distance-ordered decision-making process. However, such classical definitions of intervening opportunities have often failed to predict realistic flow volumes, particularly for short-distance flows. To overcome this problem, we have proposed a new formulation of intervening opportunities with a kernel function to introduce a fuzziness in spatial search behaviours of destinations, to develop a new variant of the radiation model. The mobility patterns resulting from the modified radiation model that included kernel-based intervening opportunities outperformed the original radiation model when fitted to four datasets of inter-regional flows.

Multiscale dynamic human mobility flow dataset in the U.S. during the COVID-19 epidemic

Understanding dynamic human mobility changes and spatial interaction patterns at different geographic scales is crucial for assessing the impacts of non-pharmaceutical interventions (such as stay-at-home orders) during the COVID-19 pandemic. In this data descriptor, we introduce a regularly-updated multiscale dynamic human mobility flow dataset across the United States, with data starting from March 1st, 2020. By analysing millions of anonymous mobile phone users' visits to various places provided by SafeGraph, the daily and weekly dynamic origin-to-destination (O-D) population flows are computed, aggregated, and inferred at three geographic scales: census tract, county, and state. There is high correlation between our mobility flow dataset and openly available data sources, which shows the reliability of the produced data. Such a high spatiotemporal resolution human mobility flow dataset at different geographic scales over time may help monitor epidemic spreading dynamics, inform public health policy, and deepen our understanding of human behaviour changes under the unprecedented public health crisis. This up-to-date O-D flow open data can support many other social sensing and transportation applications.

Multiscale dynamic human mobility flow dataset in the U.S. during the COVID-19 epidemic

Understanding dynamic human mobility changes and spatial interaction patterns at different geographic scales is crucial for assessing the impacts of non-pharmaceutical interventions (such as stay-at-home orders) during the COVID-19 pandemic. In this data descriptor, we introduce a regularly-updated multiscale dynamic human mobility flow dataset across the United States, with data starting from March 1st, 2020. By analysing millions of anonymous mobile phone users' visits to various places provided by SafeGraph, the daily and weekly dynamic origin-to-destination (O-D) population flows are computed, aggregated, and inferred at three geographic scales: census tract, county, and state. There is high correlation between our mobility flow dataset and openly available data sources, which shows the reliability of the produced data. Such a high spatiotemporal resolution human mobility flow dataset at different geographic scales over time may help monitor epidemic spreading dynamics, inform public health policy, and deepen our understanding of human behaviour changes under the unprecedented public health crisis. This up-to-date O-D flow open data can support many other social sensing and transportation applications.

Predictive limitations of spatial interaction models: a non-Gaussian analysis

We present a method to compare spatial interaction models against data based on well known statistical measures that are appropriate for such models and data. We illustrate our approach using a widely used example: commuting data, specifically from the US Census 2000. We find that the radiation model performs significantly worse than an appropriately chosen simple gravity model. Various conclusions are made regarding the development and use of spatial interaction models, including: that spatial interaction models fit badly to data in an absolute sense, that therefore the risk of over-fitting is small and adding additional fitted parameters improves the predictive power of models, and that appropriate choices of input data can improve model fit.

The education-chasing labor rush in China identified by a heterogeneous migration-network game

Despite persistent efforts in understanding the motives and patterns of human migration behaviors, little is known about the microscopic mechanism that drives migration and its association with migrant types. To fill the gap, we develop a population game model in which migrants are allowed to be heterogeneous and decide interactively on their destination, the resulting migration network emerges naturally as an Nash equilibrium and depends continuously on migrant features. We apply the model to Chinese labor migration data at the current and expected stages, aiming to quantify migration behavior and decision mode for different migrant groups and at different stages. We find the type-specific migration network differs significantly for migrants with different age, income and education level, and also differs from the aggregated network at both stages. However, a deep analysis on model performance suggests a different picture, stability exists for the decision mechanism behind the “as-if” unstable migration behavior, which also explains the relative invariance of low migration efficiency in different settings. Finally, by a classification of cities from the estimated game, we find the richness of education resources is the most critical determinant of city attractiveness for migrants, which gives hint to city managers in migration policy design.

A universal opportunity model for human mobility

Predicting human mobility between locations has practical applications in transportation science, spatial economics, sociology and many other fields. For more than 100 years, many human mobility prediction models have been proposed, among which the gravity model analogous to Newton's law of gravitation is widely used. Another classical model is the intervening opportunity (IO) model, which indicates that an individual selecting a destination is related to both the destination's opportunities and the intervening opportunities between the origin and the destination. The IO model established from the perspective of individual selection behavior has recently triggered the establishment of many new IO class models. Although these IO class models can achieve accurate prediction at specific spatiotemporal scales, an IO class model that can describe an individual's destination selection behavior at different spatiotemporal scales is still lacking. Here, we develop a universal opportunity model that considers two human behavioral tendencies: one is the exploratory tendency, and the other is the cautious tendency. Our model establishes a new framework in IO class models and covers the classical radiation model and opportunity priority selection model. Furthermore, we use various mobility data to demonstrate our model's predictive ability. The results show that our model can better predict human mobility than previous IO class models. Moreover, this model can help us better understand the underlying mechanism of the individual's destination selection behavior in different types of human mobility.

Correlations between stochastic endemic infection in multiple interacting subpopulations

Heterogeneity plays an important role in the emergence, persistence and control of infectious diseases. Metapopulation models are often used to describe spatial heterogeneity, and the transition from random- to heterogeneous-mixing is made by incorporating the interaction, or coupling, within and between subpopulations. However, such couplings are difficult to measure explicitly; instead, their action through the correlations between subpopulations is often all that can be observed. We use moment-closure methods to investigate how the coupling and resulting correlation are related, considering systems of multiple identical interacting populations on highly symmetric complex networks: the complete network, the k-regular tree network, and the star network. We show that the correlation between the prevalence of infection takes a relatively simple form and can be written in terms of the coupling, network parameters and epidemiological parameters only. These results provide insight into the effect of metapopulation network structure on endemic disease dynamics, and suggest that detailed case-reporting data alone may be sufficient to infer the strength of between population interaction and hence lead to more accurate mathematical descriptions of infectious disease behaviour.

Destination choice game: A spatial interaction theory on human mobility

With remarkable significance in migration prediction, global disease mitigation, urban planning and many others, an arresting challenge is to predict human mobility fluxes between any two locations. A number of methods have been proposed against the above challenge, including the gravity model, the intervening opportunity model, the radiation model, the population-weighted opportunity model, and so on. Despite their theoretical elegance, all models ignored an intuitive and important ingredient in individual decision about where to go, that is, the possible congestion on the way and the possible crowding in the destination. Here we propose a microscopic mechanism underlying mobility decisions, named destination choice game (DCG), which takes into account the crowding effects resulted from spatial interactions among individuals. In comparison with the state-of-the-art models, the present one shows more accurate prediction on mobility fluxes across wide scales from intracity trips to intercity travels, and further to internal migrations. The well-known gravity model is proved to be the equilibrium solution of a degenerated DCG neglecting the crowding effects in the destinations.

Gravity model explained by the radiation model on a population landscape

Understanding the mechanisms behind human mobility patterns is crucial to improve our ability to optimize and predict traffic flows. Two representative mobility models, i.e., radiation and gravity models, have been extensively compared to each other against various empirical data sets, while their fundamental relation is far from being fully understood. In order to study such a relation, we first model the heterogeneous population landscape by generating a fractal geometry of sites and then by assigning to each site a population independently drawn from a power-law distribution. Then the radiation model on this population landscape, which we call the radiation-on-landscape (RoL) model, is compared to the gravity model to derive the distance exponent in the gravity model in terms of the properties of the population landscape, which is confirmed by the numerical simulations. Consequently, we provide a possible explanation for the origin of the distance exponent in terms of the properties of the heterogeneous population landscape, enabling us to better understand mobility patterns constrained by the travel distance.

Measuring accessibility using gravity and radiation models

Since the presentation of the radiation model, much work has been done to compare its findings with those obtained from gravitational models. These comparisons always aim at measuring the accuracy with which the models reproduce the mobility described by origin-destination matrices. This has been done at different spatial scales using different datasets, and several versions of the models have been proposed to adjust to various spatial systems. However, the models, to our knowledge, have never been compared with respect to policy testing scenarios. For this reason, here we use the models to analyse the impact of the introduction of a new transportation network, a bus rapid transport system, in the city of Teresina in Brazil. We do this by measuring the estimated variation in the trip distribution, and formulate an accessibility to employment indicator for the different zones of the city. By comparing the results obtained with the two approaches, we are able to not only better assess the goodness of fit and the impact of this intervention, but also understand reasons for the systematic similarities and differences in their predictions.

Mathematical models of human mobility of relevance to malaria transmission in Africa

As Africa-wide malaria prevalence declines, an understanding of human movement patterns is essential to inform how best to target interventions. We fitted movement models to trip data from surveys conducted at 3–5 sites throughout each of Mali, Burkina Faso, Zambia and Tanzania. Two models were compared in terms of their ability to predict the observed movement patterns – a gravity model, in which movement rates between pairs of locations increase with population size and decrease with distance, and a radiation model, in which travelers are cumulatively “absorbed” as they move outwards from their origin of travel. The gravity model provided a better fit to the data overall and for travel to large populations, while the radiation model provided a better fit for nearby populations. One strength of the data set was that trips could be categorized according to traveler group – namely, women traveling with children in all survey countries and youth workers in Mali. For gravity models fitted to data specific to these groups, youth workers were found to have a higher travel frequency to large population centers, and women traveling with children a lower frequency. These models may help predict the spatial transmission of malaria parasites and inform strategies to control their spread.

Mathematical models for predicting human mobility in the context of infectious disease spread: introducing the impedance model

Background

Mathematical models of human mobility have demonstrated a great potential for infectious disease epidemiology in contexts of data scarcity. While the commonly used gravity model involves parameter tuning and is thus difficult to implement without reference data, the more recent radiation model based on population densities is parameter-free, but biased. In this study we introduce the new impedance model, by analogy with electricity. Previous research has compared models on the basis of a few specific available spatial patterns. In this study, we use a systematic simulation-based approach to assess the performances.

Methods

Five hundred spatial patterns were generated using various area sizes and location coordinates. Model performances were evaluated based on these patterns. For simulated data, comparison measures were average root mean square error (aRMSE) and bias criteria. Modeling of the 2010 Haiti cholera epidemic with a basic susceptible–infected–recovered (SIR) framework allowed an empirical evaluation through assessing the goodness-of-fit of the observed epidemic curve.

Results

The new, parameter-free impedance model outperformed previous models on simulated data according to average aRMSE and bias criteria. The impedance model achieved better performances with heterogeneous population densities and small destination populations. As a proof of concept, the basic compartmental SIR framework was used to confirm the results obtained with the impedance model in predicting the spread of cholera in Haiti in 2010.

Conclusions

The proposed new impedance model provides accurate estimations of human mobility, especially when the population distribution is highly heterogeneous. This model can therefore help to achieve more accurate predictions of disease spread in the context of an epidemic.

Electronic supplementary material

The online version of this article (10.1186/s12942-017-0115-7) contains supplementary material, which is available to authorized users.

Climate-driven endemic cholera is modulated by human mobility in a megacity

Although a differential sensitivity of cholera dynamics to climate variability has been reported in the spatially heterogeneous megacity of Dhaka, Bangladesh, the specific patterns of spread of the resulting risk within the city remain unclear. We build on an established probabilistic spatial model to investigate the importance and role of human mobility in modulating spatial cholera transmission. Mobility fluxes were inferred using a straightforward and generalizable methodology that relies on mapping population density based on a high resolution urban footprint product, and a parameter-free human mobility model. In accordance with previous findings, we highlight the higher sensitivity to the El Niño Southern Oscillation (ENSO) in the highly populated urban center than in the more rural periphery. More significantly, our results show that cholera risk is largely transmitted from the climate-sensitive core to the periphery of the city, with implications for the planning of control efforts. In addition, including human mobility improves the outbreak prediction performance of the model with an 11 month lead. The interplay between climatic and human mobility factors in cholera transmission is discussed from the perspective of the rapid growth of megacities across the developing world.

Ranking the City: The Role of Location-Based Social Media Check-Ins in Collective Human Mobility Prediction

Technological advances have led to an increasing development of data sources. Since the introduction of social networks, numerous studies on the relationships between users and their behaviors have been conducted. In this context, trip behavior is an interesting topic that can be explored via Location-Based Social Networks (LBSN). Due to the wide availability of various spatial data sources, the long-standing field of collective human mobility prediction has been revived and new models have been introduced. Recently, a parameterized model of predicting human mobility in cities, known as rank-based model, has been introduced. The model predicts the flow from an origin toward a destination using “rank” concept. However, the notion of rank has not yet been well explored. In this study, we investigate the potential of LBSN data alongside the rank concept in predicting human mobility patterns in Manhattan, New York City. For this purpose, we propose three scenarios, including: rank-distance, the number of venues between origin and destination, and a check-in weighted venue schema to compute the ranks. When trip distribution patterns are considered as a whole, applying a check-in weighting schema results in patterns that are approximately 10 percent more similar to the ground truth data. From the accuracy perspective, as the predicted numbers of trips are closer to real number of trips, the trip distribution is also enhanced by about 50 percent.