Risk, exposure and human movements

Humans are exposed to a variety of hazards as part of their everyday routines which, in turn, carry associated risks [1].

Whether the hazard is physical degradation [2], disease-bearing flies [3], or chemical toxins [4], a high degree of exposure can result in considerable risk to human health and wellbeing [5]. Unfortunately, a degree of exposure to such hazards is often unavoidable in order to obtain the resources upon which humans depend. Indeed, examples range from the financial resources obtained from attending work which potentially exposes people to influenza, to collecting basic water resources from a river surrounded by mosquito- or tsetse fly-infested bush. Given that exposure is at the heart of this problem, the study of human movements can provide important information on how exposure to such hazards varies through time and space, with potential implications in policy making and risk mitigation [6].

Gaining an insight into the dynamics of a disease can be crucial in developing forms of control and mitigation, whether this is reducing the impact of nodes or hubs which exhibit high infection rates, or disconnecting areas to limit infection pathways. One means of gaining this understanding of disease dynamics is the investigation of human movements relative to pathogen prevalence and host abundance, whether these are migratory flows over large geographical areas [7, 8], or daily movement routines of individuals within or between local settlements [9]. Although the measurement of human movements is primary, and can be captured through the use of, for example, mobile phone data [10], GPS, and individual diaries, these data are not always readily available or accessible, due to a lack of human or financial resources, or possible privacy concerns. Furthermore, the lack of available literature which considers individual human movement patterns has been highlighted [9].

Modelling human movement patterns is an alternative approach to direct measurement, and literature exists which considers ‘activity spaces’, including patterns concerning time allocations at different locations and frequency of these trips from a home site [11, 12]. Although this helps gain an understanding of people’s routines and, therefore, of periods when people might be exposed to hazards due to their location, often the journey itself is not modelled in detail. For urban settings, indoor or in-vehicle activity spaces are primary. However, where the hazard occurs outdoors, and given the degree of spatial heterogeneity in some rural environments combined with often long journeys by foot, exposure along a route is primary. As a result, this paper utilises a novel approach to model human movements in a rural setting in Africa, using a pathfinding algorithm which calculates a path between home and resource based on information about the surroundings.

Agent-based models provide a useful tool for the exploration of fine scale human movements as they, by definition, simulate the behaviour of individuals. Furthermore, the ability to incorporate spatial heterogeneity at a similarly fine scale through the incorporation of land-cover data means that the influence of an individual’s surroundings can be considered for even very short journeys. We argue that, through the implementation of an agent-based model, it is possible to estimate human movement patterns in rural settings and, thus, exposure to a given hazard, based on knowledge only of the spatial distributions of the (i) human population, (ii) resources upon which humans depend, (iii) landscape through which humans must travel in order to reach the necessary resources, and (iv) the hazard.

Agent-based models

Agent-based models are a class of computational models for exploring a system through the simulation of the interactions between individuals using simple rules, with often quite complex, emergent behaviour [13], and have been considered a “third-way” of conducting scientific research through the incorporation of both deductive and inductive approaches [14].

The use of agent-based models (ABMs) as a unique means of capturing human systems is well documented [15]. Examples range from spatially abstract environments such as Sugarscape [16], to applications which require greater detail regarding space representation and human movement, such as carnival crowd control [17] and evacuation planning [18].

ABMs focus on interactions (agent-agent, agent-environment) in ways that other modelling techniques find difficult to capture [19]. This leads to notable success for ABMs in domains like traffic and pedestrian flow where the interaction between vehicles or people can be modelled [20].

Calibrating ABMs

For ABMs to be predictively useful, the basic assumptions about movement rates and movement strategies must be well founded (e.g. cars move at the right speed, people fighting to get out of a burning plane move plausibly, etc.). As a result, there exists a strong motivation for developing methods for calibrating an agent’s movement strategies against data. As researchers must often accept data in the form that they are provided (e.g. census, surveys, mobile phone records, etc.) there is a need for flexible methods for comparing a process model (an initial theory of what people do, applied to a set of agents) to data from the real world in any arbitrary form. The detail captured in ABMs is particularly useful here because it makes possible the simulation of arbitrary data collection methods in the model, to match those in the real world, thus, allowing a direct comparison for calibration purposes.

In statistical model fitting, as practiced in much of empirical science, there are well established techniques (e.g., method of maximum likelihood) for deciding which of a suite of possible statistical models gives the best fit to data. However, while conceptual frameworks for spatially explicit ABMs in epidemiology have been formulated [21] and explored [22], at present, little information is available in the literature concerning how real world data can be used to calibrate simulated human movements in an epidemiological ABM. Thus, a challenge to the wider acceptance of ABMs is the lack of universally agreed methods for calibrating them against data. Given the additional issue that calibration data are not always available for ABM studies due to the issues of cost and accessibility discussed previously, ABM construction can be hindered, and this could be one of the reasons why there are relatively few studies presenting epidemiological ABMs in the literature. As a result of these factors, many ABMs are not calibrated to data at all and are left as suggestive, approximate theoretical exercises.

Recent developments in the study of spatial epidemiology have seen ABMs applied to systems involving multiple classes of agents (e.g., human, livestock, fly) to investigate disease transmission [23]. As with the examples of social systems provided above, the resolution at which movements through space and time need to be represented varies in the field of epidemiology. When considering the average flows of people at a national or continental scale over a long period of time (when investigating, e.g., the large area prevalence of a disease such as malaria) modelling the daily frequency and direction of individual’s movements may not be that useful. However, when investigating a vector-borne disease in a sparsely populated environment at a local scale, the spatial locations of hosts and vectors are likely to be of fundamental importance to disease dynamics [24]. Indeed, capturing the spatial heterogeneity of a study area in landscape epidemiology can be an integral component of a realistic disease simulation [25].

As part of an existing interest in modelling the epidemiology of Human African Trypanosomiasis (HAT, or more commonly, sleeping sickness) and Animal African Trypanosomiasis (AAT, also referred to as Nagana), we previously constructed a simplified ABM of humans, cattle and tsetse flies [26]. As sleeping sickness is a neglected tropical disease, the prospect for development of new, more effective treatments in the near future is limited, with out-of-date, difficult to administer, and partially validated treatments currently in use [27–29]. Unfortunately, where tools are available, HAT is rarely prioritised due to competing public health interests [30]. As a result, public health policy is critical, and appropriate control methods will require a greater understanding of disease dynamics [31]. ABMs used wisely can potentially lead to better informed public health policy. However, an accurately calibrated model is required to make any simulated predictions of disease prevalence sufficiently representative and, thus, potentially useful as a decision-support tool.

This paper demonstrates the potential use of ABMs as tools for generating human movement patterns, which could subsequently be used for a range of potential applications including assessment of individual exposure to biting insects such as mosquitoes and tsetse flies, contact probabilities and, thus, transmission pathways and potential. The approach depends only on an initial distribution of agents, resource locations, and a given landscape (capturing the difficulty of traversing elements in the landscape), and fairly well accepted assumptions about people’s daily resource requirements. In this study area, these include frequent trips to water and for the collection of firewood, children’s trips to school in the morning or afternoon, less frequent trips to market, and work in the fields. Thus, this paper proposes for the first time the use of ABMs to simulate human movements based only on widely available geospatial datasets, as an alternative to expensive measurement of human movements, for use in epidemiological studies. The implication is that plausible movement patterns can be generated for any similar location, with limited need for human movement data. Using extensive household survey data from the Luangwa Valley, Zambia, a method for calibrating human agent movements against real world data in epidemiological ABMs was explored, demonstrating that the ABM method proposed here is able to predict human movements accurately.

Land Cover Classification and Cost Surface

When a person moves from A to B, their chosen route is often influenced by the terrain ahead of them. To incorporate this decision process into the ABM model, a cost surface of the study area was generated. Specifically, a Landsat image of the study area with a spatial resolution of 30 m was used to produce a land cover classification, dividing the region into areas of bush (high cost), farmland and cleared land (low cost). These classes allow different speeds of human movement (4 or 5 or 6 km hr^-1) based on modifications of the movement speeds used in [32] and, therefore, need to be considered as potential facilitators or inhibitors when determining human routes to resources. Subsequently, where agent routes traverse different classes of land cover, these data can be used to define the speed at which people move through them. The incorporation of this technique may be important as exposure to different risks can be reduced or heightened depending on the precise route of human movement, but also by how long it takes for an individual to cross through one of these zones. Although it is acknowledged that variations in elevation can play a role in varying path choice and movement speed, the settled area under investigation is relatively flat with only a gentle south-to-north slope, and thus elevation was not considered in this iteration of the model as a result.

A* Pathfinding Algorithm

Many different methods can be used to simulate human movements in an ABM. At two extremes, one could simulate linear movement by programming the agent to move along a Euclidean path between start and goal, or use an implementation of Dijkstra’s flood fill algorithm to ensure the least cost route is taken from cell to cell or pixel to pixel, regardless of how direct it is. In real world terms, the first approach simulates a person who wants to get from point A to point B as fast as possible, assuming that there are no obstacles in the way, and that the terrain underfoot is uniform, whereas the second approach simulates a person who will get from A to B eventually, at minimal cost to them (e.g. avoiding unfavourable land cover etc.).

Something more complicated than either of the above options is likely to be a better match to reality, and this requires finding a balance between the two. Indeed, while it is often important to move as directly as possible to a goal, certain areas along this direct route may be impassable or at a higher cost than the individual is willing to allow.

Although numerous pathfinding algorithms have been used in the literature, A* [33] was used in this research as it was considered to be the technique which most accurately replicates the process by which a human would devise a route to goal, while having the added advantage of being computationally economical.

By combining a Euclidean distance heuristic (i.e. the straight line route from start to goal), with the previously described cost surface, a search which resembles a ‘directed flood fill’ is produced. In this sense, while the cost surface between different pixels from start to goal remains constant, the most efficient straight line route is preferred. However, when a higher cost region is encountered along the path, the algorithm will decide whether the optimal route is to travel around the high cost area, or through it, in order to continue moving towards the goal.

Questionnaire Data

Information regarding the time people take to collect domestic water was collected as part of a wider human movement questionnaire in the Luangwa Valley, Zambia, in June 2013 (S1 Appendix). The valley is an extension of the Great Rift Valley in East Africa, and lies across the Eastern and Northern Provinces of Zambia Fig 2. The survey was administered to a sample of 94 individual households. Individual-level information such as sex, age and relationship to household head was collected, along with their village role, and the amount of time an individual thought it took them to make a single journey to the water source of their choice. Information was also recorded on the frequency of these collections, including number of collections per day, and whether these occur in the morning, afternoon or evening. While the sample’s household locations were identified using GPS, along with the locations of a number of boreholes, as the data collectors could not accompany each individual on a trip to water, the exact location of different riverine water sources was not recorded.

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Fig 2. Sample village sites (red circles) and observed boreholes (blue circles) in the study area, Luangwa Valley, Zambia (Produced using Landsat 7 imagery from USGS).

https://doi.org/10.1371/journal.pone.0139505.g002

Multi-Layer Input Map

The GPS coordinates obtained for household location were overlain on fine spatial resolution Bing aerial imagery, accessed through the open layers plug-in in QGIS. The previously mentioned 30 m spatial resolution land cover classification was then overlain on this finer spatial resolution imagery, before cross-referencing and editing through the digitizing of river and road detail which was too detailed to be captured at the coarser spatial resolution. The product was a multi-layer input map for the model, comprising spatial information on household, river, road and borehole locations, along with pixels allocated to the classes of bare ground, forest and crop growing fields, at a spatial resolution of 11 m. Fig 3 shows a sample section of the land cover classification layer for the model.

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Fig 3. Sample section of the land classification map, with forest (green), crop (off-white), and bare land (magenta) areas highlighted.

Road and river are represented by gold and blue lines respectively.

https://doi.org/10.1371/journal.pone.0139505.g003

Program Description

Two separate computer programs were used to produce the observed results. Firstly, a program was written to implement multiple heuristics in the A* algorithm, producing different paths from the 94 households to different riverine and borehole water sources. This was implemented using the Iridis 3 supercomputer at the University of Southampton. Secondly, an ABM was constructed to test how long it takes agents to travel along each of these paths, given the impedance resulting from the cost surface. These programs are described in greater detail in the methodology.

A* Algorithm

The land cover map introduced above was used to produce a grid of cells with values associated to their cost in terms of human movement speed. For example, road was allocated the least cost, followed by crop and bare land, with bush allocated the highest cost. While river levels are highly seasonally dependent, river cells were considered impassable in this study, reflecting river levels in the rainy season, where human exposure is likely to be higher due to more favourable conditions for the tsetse fly. Whilst beyond the scope of this study, it would be possible to adjust this assumption, varying the weight applied to river cells in order to reflect seasonal changes in how ‘passable’ the river is. Land cells that neighbour the river were collated and a random sample of 1000 of these was used as a set of potential riverine watering sites. Agents were allowed to choose randomly between the three sites closest to their village as their resource goal.

In each iteration of the model, the algorithm assessed the cost of moving to each of its eight neighbouring cells based on the summation of two factors; g and h: (1) (2)

The g score represents the cost of movement between the start and the current cell, which is known and includes accurate land surface costs thus far, while the h score is the remaining linear distance to the goal. C represents the cost of moving from the current cell to the next (potential) cell, which varies depending on the land cover. α represents the weighting of the movement cost, with a higher value of α resulting in the algorithm favouring low cost cells such as road, over the most direct route.

At each iteration the optimal cell is selected from the eight neighbours, which represents the best path to take (lowest f(n)), and made into the ‘child’ of the current cell before it itself becomes the ‘current cell’ in the next iteration. This means that the algorithm creates a trail of cells that results in the path so far, which is linked by parent-child connections. By taking this approach, this also means that there could be multiple potential paths during the process. When one of these potential paths reaches the goal, the parent-child connections from goal to start are declared the best possible route, and the algorithm ends by creating a list of these cells, along with the corresponding cell land cover classes.

As the construction of these paths is a variable under investigation, how much of an impact the land cover has on the chosen path (i.e. how far will an agent travel off the Euclidean route to walk on, e.g., road instead of crop) was varied for multiple runs.

In the real world, when a person chooses a route of travel, there is often a conflict between the most direct path, and the ‘easiest’ path to the destination, often resulting in a compromise. This paper seeks to identify the appropriate balance of these two factors in this investigation by varying α. α was varied from 0–45, providing a sufficient range of weightings to identify the optimum choice. The cost (C in the above equation) was multiplied by α before adding to the g score in different runs to give a greater weighting to certain land covers. Therefore, as the value of α increases, the algorithm will increasingly favour low cost routes at the expense of direct travel. An α = 0 run was included as a control as this represents the Euclidean distance. h was multiplied by 10 in each run for computational efficiency, removing the decimal number associated with diagonal moves. Future references to the different variations of the algorithm, and the results they produce, will be by their respective h and g values in the form: H10Gα. Fig 4 shows an example path produced using the algorithm in the study area of this investigation.

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Fig 4. Example path produced using the A* and land classification between arbitrary points.

Arbitrary points were used to emphasise how the algorithm diverts the path around a prominent obstacle; in this case, the river itself (Produced using Bing aerial imagery).

https://doi.org/10.1371/journal.pone.0139505.g004

Agent-Based Model

Initially, the 11 m spatial resolution aerial imagery was made into a graphical interface to observe the subsequent simulation running using the Tkinter package in Python 2.7. The cost surface land cover information, along with the coordinates of villages, boreholes and potential watering sites were incorporated as arrays. Populations were then initialised, placing 5000 agents randomly across the villages in the simulation. A large number such as this was used so that each village would be populated and therefore a comparative simulated distribution of walk times could be produced. Iterations of the simulation were used to represent clock time (18 seconds per iteration), where an agent would move between their home village, and a watering site (either borehole, or one of the three closest riverine sites) along the previously calculated A* paths. 18 second iterations, or 4800 iteration days, were used so that the temporal resolution of the model was fine enough to include the shortest trips of agents to water, which can be less than 5 minutes. Movement speed between cells was dictated by the land cover of the cell which the agent was about to move to, so that the agent moves faster through preferable terrain such as road, and slower through the other types of land cover. The number of steps an agent takes per iteration was governed by the maximum distance an agent could travel in this period, which was defined by the land cover of the cells across this distance. The number of cells moved in one time step would be at a maximum if an agent encountered only road cells (resulting in an approximate speed of 6 km^-1). Conversely, an agent would cover fewer cells per time step should some of these cells be, for example, bush, reducing their speed. The fewest cells covered or lowest speed would be associated with an agent encountering only forest cells. Certain combinations of cells within a particular time step may not meet the distance threshold exactly. Should the distance travelled be less than the threshold, and the difference less than a step size, a random draw was used to decide whether another step was taken in this iteration. The time taken for the agent to travel a single journey from village to the water resource goal was recorded in minutes. Return trip times were not considered in this investigation due to the form of the questionnaire data, but also due to the difficulty in quantifying the reduction in walk speed which could result from carrying a heavy load of water.

The results were divided into bins to allow a Chi-squared analysis, comparing the distributions of the simulation results and the questionnaire data. The simulation was run again for a single agent per village to allow analysis of the individual error between the simulation and real world data.