Evaluating Spatial Interaction Models for Regional Mobility in Sub-Saharan Africa

Simple spatial interaction models of human mobility based on physical laws have been used extensively in the social, biological, and physical sciences, and in the study of the human dynamics underlying the spread of disease. Recent analyses of commuting patterns and travel behavior in high-income countries have led to the suggestion that these models are highly generalizable, and as a result, gravity and radiation models have become standard tools for describing population mobility dynamics for infectious disease epidemiology. Communities in Sub-Saharan Africa may not conform to these models, however; physical accessibility, availability of transport, and cost of travel between locations may be variable and severely constrained compared to high-income settings, informal labor movements rather than regular commuting patterns are often the norm, and the rise of mega-cities across the continent has important implications for travel between rural and urban areas. Here, we first review how infectious disease frameworks incorporate human mobility on different spatial scales and use anonymous mobile phone data from nearly 15 million individuals to analyze the spatiotemporal dynamics of the Kenyan population. We find that gravity and radiation models fail in systematic ways to capture human mobility measured by mobile phones; both severely overestimate the spatial spread of travel and perform poorly in rural areas, but each exhibits different characteristic patterns of failure with respect to routes and volumes of travel. Thus, infectious disease frameworks that rely on spatial interaction models are likely to misrepresent population dynamics important for the spread of disease in many African populations.     

Decelerating spread of West Nile virus by percolation in a heterogeneous urban landscape

Vector-borne diseases are emerging and re-emerging in urban environments throughout the world, presenting an increasing challenge to human health and a major obstacle to development. Currently, more than half of the global population is concentrated in urban environments, which are highly heterogeneous in the extent, degree, and distribution of environmental modifications. Because the prevalence of vector-borne pathogens is so closely coupled to the ecologies of vector and host species, this heterogeneity has the potential to significantly alter the dynamical systems through which pathogens propagate, and also thereby affect the epidemiological patterns of disease at multiple spatial scales. One such pattern is the speed of spread. Whereas standard models hold that pathogens spread as waves with constant or increasing speed, we hypothesized that heterogeneity in urban environments would cause decelerating travelling waves in incipient epidemics. To test this hypothesis, we analysed data on the spread of West Nile virus (WNV) in New York City (NYC), the 1999 epicentre of the North American pandemic, during annual epizootics from 2000-2008. These data show evidence of deceleration in all years studied, consistent with our hypothesis. To further explain these patterns, we developed a spatial model for vector-borne disease transmission in a heterogeneous environment. An emergent property of this model is that deceleration occurs only in the vicinity of a critical point. Geostatistical analysis suggests that NYC may be on the edge of this criticality. Together, these analyses provide the first evidence for the endogenous generation of decelerating travelling waves in an emerging infectious disease. Since the reported deceleration results from the heterogeneity of the environment through which the pathogen percolates, our findings suggest that targeting control at key sites could efficiently prevent pathogen spread to remote susceptible areas or even halt epidemics.     

Using a Network Model to Assess Risk of Forest Pest Spread via Recreational Travel

Long-distance dispersal pathways, which frequently relate to human activities, facilitate the spread of alien species. One pathway of concern in North America is the possible spread of forest pests in firewood carried by visitors to campgrounds or recreational facilities. We present a network model depicting the movement of campers and, by extension, potentially infested firewood. We constructed the model from US National Recreation Reservation Service data documenting more than seven million visitor reservations (including visitors from Canada) at campgrounds nationwide. This bi-directional model can be used to identify likely origin and destination locations for a camper-transported pest. To support broad-scale decision making, we used the model to generate summary maps for 48 US states and seven Canadian provinces that depict the most likely origins of campers traveling from outside the target state or province. The maps generally showed one of two basic spatial patterns of out-of-state (or out-of-province) origin risk. In the eastern United States, the riskiest out-of-state origin locations were usually found in a localized region restricted to portions of adjacent states. In the western United States, the riskiest out-of-state origin locations were typically associated with major urban areas located far from the state of interest. A few states and the Canadian provinces showed characteristics of both patterns. These model outputs can guide deployment of resources for surveillance, firewood inspections, or other activities. Significantly, the contrasting map patterns indicate that no single response strategy is appropriate for all states and provinces. If most out-of-state campers are traveling from distant areas, it may be effective to deploy resources at key points along major roads (e.g., interstate highways), since these locations could effectively represent bottlenecks of camper movement. If most campers are from nearby areas, they may have many feasible travel routes, so a more widely distributed deployment may be necessary.     

Raccoon Social Networks and the Potential for Disease Transmission

Raccoons are an important vector of rabies and other pathogens. The degree to which these pathogens can spread through a raccoon population should be closely linked to association rates between individual raccoons. Most studies of raccoon sociality have found patterns consistent with low levels of social connectivity within populations, thus the likelihood of direct pathogen transmission between raccoons is theoretically low. We used proximity detecting collars and social network metrics to calculate the degree of social connectivity in an urban raccoon population for purposes of estimating potential pathogen spread. In contrast to previous assumptions, raccoon social association networks were highly connected, and all individuals were connected to one large social network during 15 out of 18 months of study. However, these metrics may overestimate the potential for a pathogen to spread through a population, as many of the social connections were based on relatively short contact periods. To more closely reflect varying probabilities of pathogen spread, we censored the raccoon social networks based on the total amount of time spent in close proximity between two individuals per month. As this time criteria for censoring the social networks increased from one to thirty minutes, corresponding measures of network connectivity declined. These findings demonstrate that raccoon populations are much more tightly connected than would have been predicted based on previous studies, but also point out that additional research is needed to calculate more precise transmission probabilities by infected individuals, and determine how disease infection changes normal social behaviors.     

Deriving fine-scale models of human mobility from aggregated origin-destination flow data

The spatial dynamics of epidemics are fundamentally affected by patterns of human mobility. Mobile phone call detail records (CDRs) are a rich source of mobility data, and allow semi-mechanistic models of movement to be parameterised even for resource-poor settings. While the gravity model typically reproduces human movement reasonably well at the administrative level spatial scale, past studies suggest that parameter estimates vary with the level of spatial discretisation at which models are fitted. Given that privacy concerns usually preclude public release of very fine-scale movement data, such variation would be problematic for individual-based simulations of epidemic spread parametrised at a fine spatial scale. We therefore present new methods to fit fine-scale mathematical mobility models (here we implement variants of the gravity and radiation models) to spatially aggregated movement data and investigate how model parameter estimates vary with spatial resolution. We use gridded population data at 1km resolution to derive population counts at different spatial scales (down to ∼ 5km grids) and implement mobility models at each scale. Parameters are estimated from administrative-level flow data between overnight locations in Kenya and Namibia derived from CDRs: where the model spatial resolution exceeds that of the mobility data, we compare the flow data between a particular origin and destination with the sum of all model flows between cells that lie within those particular origin and destination administrative units. Clear evidence of over-dispersion supports the use of negative binomial instead of Poisson likelihood for count data with high values. Radiation models use fewer parameters than the gravity model and better predict trips between overnight locations for both considered countries. Results show that estimates for some parameters change between countries and with spatial resolution and highlight how imperfect flow data and spatial population distribution can influence model fit.     

Social encounter networks: characterizing Great Britain

A major goal of infectious disease epidemiology is to understand and predict the spread of infections within human populations, with the intention of better informing decisions regarding control and intervention. However, the development of fully mechanistic models of transmission requires a quantitative understanding of social interactions and collective properties of social networks. We performed a cross-sectional study of the social contacts on given days for more than 5000 respondents in England, Scotland and Wales, through postal and online survey methods. The survey was designed to elicit detailed and previously unreported measures of the immediate social network of participants relevant to infection spread. Here, we describe individual-level contact patterns, focusing on the range of heterogeneity observed and discuss the correlations between contact patterns and other socio-demographic factors. We find that the distribution of the number of contacts approximates a power-law distribution, but postulate that total contact time (which has a shorter-tailed distribution) is more epidemiologically relevant. We observe that children, public-sector and healthcare workers have the highest number of total contact hours and are therefore most likely to catch and transmit infectious disease. Our study also quantifies the transitive connections made between an individual''s contacts (or clustering); this is a key structural characteristic of social networks with important implications for disease transmission and control efficacy. Respondents'' networks exhibit high levels of clustering, which varies across social settings and increases with duration, frequency of contact and distance from home. Finally, we discuss the implications of these findings for the transmission and control of pathogens spread through close contact.     

Predictability of Road Traffic and Congestion in Urban Areas

Mitigating traffic congestion on urban roads, with paramount importance in urban development and reduction of energy consumption and air pollution, depends on our ability to foresee road usage and traffic conditions pertaining to the collective behavior of drivers, raising a significant question: to what degree is road traffic predictable in urban areas? Here we rely on the precise records of daily vehicle mobility based on GPS positioning device installed in taxis to uncover the potential daily predictability of urban traffic patterns. Using the mapping from the degree of congestion on roads into a time series of symbols and measuring its entropy, we find a relatively high daily predictability of traffic conditions despite the absence of any priori knowledge of drivers'' origins and destinations and quite different travel patterns between weekdays and weekends. Moreover, we find a counterintuitive dependence of the predictability on travel speed: the road segment associated with intermediate average travel speed is most difficult to be predicted. We also explore the possibility of recovering the traffic condition of an inaccessible segment from its adjacent segments with respect to limited observability. The highly predictable traffic patterns in spite of the heterogeneity of drivers'' behaviors and the variability of their origins and destinations enables development of accurate predictive models for eventually devising practical strategies to mitigate urban road congestion.     

Mesoscopic structure and social aspects of human mobility

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 typical daily activity, along with subsidiary habitats representing additional travel. These habitats do not correspond to typical contexts such as home or work. The temporal evolution of mobility within habitats, which constitutes most motion, is universal across habitats and exhibits scaling patterns both distinct from all previous observations and unpredicted by current models. The delay to enter subsidiary habitats is a primary factor in the spatiotemporal growth of human travel. Interestingly, habitats correlate with non-mobility dynamics such as communication activity, implying that habitats may influence processes such as information spreading and revealing new connections between human mobility and social networks.     

Obesity and the Built Environment: A Reappraisal

The built environment (BE) has been viewed as an important determinant of health. Numerous studies have linked BE exposure, captured using a variety of methods, to diet quality and to area prevalence of obesity, diabetes, and cardiovascular disease. First‐generation studies defined the neighborhood BE as the area around the home. Second‐generation studies turned from home‐centric to person‐centric BE measures, capturing an individual’s movements in space and time. Those studies made effective uses of global positioning system tracking devices and mobile phones, sometimes coupled with accelerometers and remote sensors. Activity space metrics explored travel paths, modes, and destinations to assess BE exposure that was both person and context specific. However, as measures of the contextual exposome have become ever more fine‐grained and increasingly complex, connections to long‐term chronic diseases with complex etiologies, such as obesity, are in danger of being lost. Furthermore, few studies on obesity and the BE have included intermediate energy balance behaviors, such as diet and physical activity, or explored the potential roles of social interactions or psychosocial pathways. Emerging survey‐based applications that identify habitual destinations and associated travel patterns may become the third generation of tools to capture health‐relevant BE exposures in the long term.     

Spatial spread of an epidemic through public transportation systems with a hub

This article investigates an epidemic spreading among several locations through a transportation system, with a hub connecting these locations. Public transportation is not only a bridge through which infections travel from one location to another but also a place where infections occur since individuals are typically in close proximity to each other due to the limited space in these systems. A mathematical model is constructed to study the spread of an infectious disease through such systems. A variant of the next generation method is proposed and used to provide upper and lower bounds of the basic reproduction number for the model. Our investigation indicates that increasing transportation efficiency, and improving sanitation and ventilation of the public transportation system decrease the chance of an outbreak occurring. Moreover, discouraging unnecessary travel during an epidemic also decreases the chance of an outbreak. However, reducing travel by infectives while allowing susceptibles to travel may not be enough to avoid an outbreak.     

Social mixing patterns in rural and urban areas of southern China

A dense population, global connectivity and frequent human–animal interaction give southern China an important role in the spread and emergence of infectious disease. However, patterns of person-to-person contact relevant to the spread of directly transmitted infections such as influenza remain poorly quantified in the region. We conducted a household-based survey of travel and contact patterns among urban and rural populations of Guangdong, China. We measured the character and distance from home of social encounters made by 1821 individuals. Most individuals reported 5–10 h of contact with around 10 individuals each day; however, both distributions have long tails. The distribution of distance from home at which contacts were made is similar: most were within a kilometre of the participant''s home, while some occurred further than 500 km away. Compared with younger individuals, older individuals made fewer contacts which tended to be closer to home. There was strong assortativity in age-based contact rates. We found no difference between the total number or duration of contacts between urban and rural participants, but urban participants tended to make contacts closer to home. These results can improve mathematical models of infectious disease emergence, spread and control in southern China and throughout the region.     

On the treatment of airline travelers in mathematical models

The global spread of infectious diseases is facilitated by the ability of infected humans to travel thousands of miles in short time spans, rapidly transporting pathogens to distant locations. Mathematical models of the actual and potential spread of specific pathogens can assist public health planning in the case of such an event. Models should generally be parsimonious, but must consider all potentially important components of the system to the greatest extent possible. We demonstrate and discuss important assumptions relative to the parameterization and structural treatment of airline travel in mathematical models. Among other findings, we show that the most common structural treatment of travelers leads to underestimation of the speed of spread and that connecting travel is critical to a realistic spread pattern. Models involving travelers can be improved significantly by relatively simple structural changes but also may require further attention to details of parameterization.     

Connecting the dots: Stopover strategies of an intercontinental migratory songbird in the context of the annual cycle

The phases of the annual cycle for migratory species are inextricably linked. Yet, less than five percent of ecological studies examine seasonal interactions. In this study, we utilized stable hydrogen isotopes to geographically link individual black‐and‐white warblers (Mniotilta varia) captured during spring migration with breeding destinations to understand a migrant's stopover strategy in the context of other phases of the annual cycle. We found that stopover strategy is not only a function of a bird's current energetic state, but also the distance remaining to breeding destination and a bird's time‐schedule, which has previously been linked to habitat conditions experienced in the preceding phase of the annual cycle. Birds in close proximity to their breeding destination accumulate additional energy reserves prior to arrival on the breeding grounds, as reflected by higher migratory condition upon arrival, higher refueling rates measured via blood plasma metabolites, and longer stopover durations compared to birds migrating to breeding destinations farther from the stopover site. However, late birds near their breeding destination were more likely to depart on the day of arrival (i.e., transients), and among birds that stopped over at the site, the average duration of stopover was almost half the time of early conspecifics, suggesting late birds are trying to catch‐up with the overall time‐schedule of migration for optimal arrival time on the breeding grounds. In contrast, birds with long distances remaining to breeding destinations were more likely to depart on the day of arrival and primarily used stopover to rest before quickly resuming migration, adopting similar strategies regardless of a bird's time‐schedule. Our study demonstrates that migrants adjust their en route strategies in relation to their time‐schedule and distance remaining to their breeding destination, highlighting that strategies of migration should be examined in the context of other phases of the annual cycle.     

Travel patterns in China

The spread of infectious disease epidemics is mediated by human travel. Yet human mobility patterns vary substantially between countries and regions. Quantifying the frequency of travel and length of journeys in well-defined population is therefore critical for predicting the likely speed and pattern of spread of emerging infectious diseases, such as a new influenza pandemic. Here we present the results of a large population survey undertaken in 2007 in two areas of China: Shenzhen city in Guangdong province, and Huangshan city in Anhui province. In each area, 10,000 randomly selected individuals were interviewed, and data on regular and occasional journeys collected. Travel behaviour was examined as a function of age, sex, economic status and home location. Women and children were generally found to travel shorter distances than men. Travel patterns in the economically developed Shenzhen region are shown to resemble those in developed and economically advanced middle income countries with a significant fraction of the population commuting over distances in excess of 50 km. Conversely, in the less developed rural region of Anhui, travel was much more local, with very few journeys over 30 km. Travel patterns in both populations were well-fitted by a gravity model with a lognormal kernel function. The results provide the first quantitative information on human travel patterns in modern China, and suggest that a pandemic emerging in a less developed area of rural China might spread geographically sufficiently slowly for containment to be feasible, while spatial spread in the more economically developed areas might be expected to be much more rapid, making containment more difficult.     

Tree diseases and landscape processes: the challenge of landscape pathology

Forest pathology inherently involves a landscape perspective, because tree pathogens propagate according to heterogeneous spatial patterns of flow and isolation. Landscape pathology is a field that is now emerging from the transdisciplinary cooperation of forest pathologists with landscape ecologists. Here, we review recent broad-scale assessments of tree disease risk, investigations of site and host preferences for several root rot pathogens, and regional historical analyses of pathogen outbreak in plantations. Crucial topics include fragmentation effects on pathogen spread and geophysical features that predispose forest patches to disease expression. Recent methodological developments facilitate the spatially explicit analysis of reciprocal coarse-scale relationships among hosts and pathogens. Landscape pathology studies fill a significant research gap in the context of our understanding of sustainable forest management, the introduction of exotic organisms and how climate change might affect the spread of disease.     

Human mobility patterns predict divergent epidemic dynamics among cities

The epidemic dynamics of infectious diseases vary among cities, but it is unclear how this is caused by patterns of infectious contact among individuals. Here, we ask whether systematic differences in human mobility patterns are sufficient to cause inter-city variation in epidemic dynamics for infectious diseases spread by casual contact between hosts. We analyse census data on the mobility patterns of every full-time worker in 48 Canadian cities, finding a power-law relationship between population size and the level of organization in mobility patterns, where in larger cities, a greater fraction of workers travel to work in a few focal locations. Similarly sized cities also vary in the level of organization in their mobility patterns, equivalent on average to the variation expected from a 2.64-fold change in population size. Systematic variation in mobility patterns is sufficient to cause significant differences among cities in infectious disease dynamics—even among cities of the same size—according to an individual-based model of airborne pathogen transmission parametrized with the mobility data. This suggests that differences among cities in host contact patterns are sufficient to drive differences in infectious disease dynamics and provides a framework for testing the effects of host mobility patterns in city-level disease data.     

Using geotagged photographs and GIS analysis to estimate visitor flows in natural areas

Protected area management requires detailed information about visitors’ travel patterns. Unfortunately, methods commonly applied to obtain this information (e.g. monitoring, simulation) are expensive and time consuming. As a result, for many protected areas worldwide there are no reliable data upon which management actions (e.g. trail maintenance, introduction of use limits) can be based. Today georeferenced material shared on the Internet (e.g. geotagged photographs, GPS tracks) provides a new valuable source of information about people's movements, though its low density (e.g. few geotagged photographs per unit area) in natural areas has discouraged applications in such contexts so far. We propose a new approach that uses geotagged photographs to identify popular locations, and a gravity model to estimate the volume of visitor flows from access points (e.g. parking lots, bus stops) to those locations. The model, which assumes volumes to be proportional to the popularity of access points and destinations, and inversely proportional to the travel time for going from one to the other, is set up in a GIS environment and calibrated by means of actual visitor counts over a set of locations in the study area.Results of a first application to the Dolomites UNESCO World Heritage Site (Italy) are encouraging as the model provided good estimates and a consistent map of visitor flows. The method enables park managers to roughly estimate visitor flows over large trail networks with only limited field work required. Future applications may include the analysis of off-trail movements to predict the intensity of trampling.     

The Cost of Simplifying Air Travel When Modeling Disease Spread

Background

Air travel plays a key role in the spread of many pathogens. Modeling the long distance spread of infectious disease in these cases requires an air travel model. Highly detailed air transportation models can be over determined and computationally problematic. We compared the predictions of a simplified air transport model with those of a model of all routes and assessed the impact of differences on models of infectious disease.

Methodology/Principal Findings

Using U.S. ticket data from 2007, we compared a simplified “pipe” model, in which individuals flow in and out of the air transport system based on the number of arrivals and departures from a given airport, to a fully saturated model where all routes are modeled individually. We also compared the pipe model to a “gravity” model where the probability of travel is scaled by physical distance; the gravity model did not differ significantly from the pipe model. The pipe model roughly approximated actual air travel, but tended to overestimate the number of trips between small airports and underestimate travel between major east and west coast airports. For most routes, the maximum number of false (or missed) introductions of disease is small (<1 per day) but for a few routes this rate is greatly underestimated by the pipe model.

Conclusions/Significance

If our interest is in large scale regional and national effects of disease, the simplified pipe model may be adequate. If we are interested in specific effects of interventions on particular air routes or the time for the disease to reach a particular location, a more complex point-to-point model will be more accurate. For many problems a hybrid model that independently models some frequently traveled routes may be the best choice. Regardless of the model used, the effect of simplifications and sensitivity to errors in parameter estimation should be analyzed.     

Individual differences in searching behaviour and spatial foraging consistency in a central place marine predator

Consistent intra‐population variability in foraging behaviour is found among a wide range of taxa. Such foraging specialisations are common among marine vertebrates, yet it is not clear how individuals repeatedly locate prey or foraging sites at ocean‐wide scales. Using GPS and time‐depth loggers we studied the fine‐scale foraging behaviour of central‐place northern gannets Morus bassanus at two large colonies. First, we estimated the degree of consistency in individual foraging routes and sites across repeated trips. Second, we tested for individual differences in searching behaviour in response to environmental covariates using reaction norms, estimated from mixed effect models. Adult gannets tracked over multiple foraging trips showed repeatable between‐individual differences in terminal points and departure angles of foraging trips, but low repeatability in trip duration and trip length. Importantly, individual birds showed highly repeatable dive locations, with consistently different environmental conditions (such as copepod abundance), suggesting a high degree of foraging site specialisation. Gannets also showed between‐individual differences in searching behaviour along environmental gradients, such that individuals intensified searching under different conditions. Together these results suggest that widespread individual foraging consistency may represent specialisation and be linked with individual responses to environmental conditions. Such divergent searching behaviour could provide a mechanism by which consistent foraging behaviour arises and is maintained among animals that forage across large spatial scales.     

The dynamics of sexual contact networks: effects on disease spread and control

Sexually transmitted pathogens persist in populations despite the availability of biomedical interventions and knowledge of behavioural changes that would reduce individual-level risk. While behavioural risk factors are shared between many sexually transmitted infections, the prevalence of these diseases across different risk groups varies. Understanding this heterogeneity and identifying better control strategies depends on an improved understanding of the complex social contact networks over which pathogens spread. To date, most efforts to study the impact of sexual network structure on disease dynamics have focused on static networks. However, the interaction between the dynamics of partnership formation and dissolution and the dynamics of transmission plays a role, both in restricting the effective network accessible to the pathogen, and in modulating the transmission dynamics. We present a simple method to simulate dynamical networks of sexual partnerships. We inform the model using survey data on sexual attitudes and lifestyles, and investigate how the duration of infectiousness changes the effective contact network over which disease may spread. We then simulate several control strategies: screening, vaccination and behavioural interventions. Previous theory and research has advanced the importance of core groups for spread and control of STD. Our work is consistent with the importance of core groups, but extends this idea to consider how the duration of infectiousness associated with a particular pathogen interacts with host behaviours to define these high risk subpopulations. Characteristics of the parts of the network accessible to the pathogen, which represent the network structure of sexual contacts from the “point of view” of the pathogen, are substantially different from those of the network as a whole. The pathogen itself plays an important role in determining this effective network structure; specifically, we find that if the pathogen’s duration of infectiousness is short, infection is more concentrated in high-activity, high-concurrency individuals even when all other factors are held constant. Widespread screening programmes would be enhanced by follow-up interventions targeting higher-risk individuals, because screening shortens the expected duration of infectiousness and causes a greater relative decrease in prevalence among lower-activity than in higher-activity individuals. Even for pathogens with longer durations of infectiousness, our findings suggest that targeting vaccination and behavioural interventions towards high-activity individuals provides comparable benefits to population-wide interventions.