» WP2: Spatially structured models and human mobility

WP2: Spatially structured models and human mobility

The key focus of workpackage 2 is the construction of more sophisticated models for disease dynamics across multiple spatial scales based on increasing scientific insights gained by approaching the dynamic and structural components that shape spatial disease dynamics from multiple angles. This central goal is intimately tied to workpackage 1 that focuses on models of single populations and inter-individual contact networks. Furthermore the investigations performed in WP2 will be the conceptual foundation of the development of epidemic modeling platform (WP4). The activities described below were geared towards a better theoretical understanding of the building blocks of realistic, reliable and predictive models for spatial disease dynamics.

Theme 1. Structure of Human Mobility Networks

Considerable effort has in WP2 has been devoted to extend our understanding of mobility and transportation networks. Based on the notion that spatio-temporal patterns of disease dynamics are predominantly shaped by topological features of the underlying multi-scale mobility networks the projects described below were initiated in order to reduce the structural complexity of mobility networks and consequently reduce the complexity of the disease dynamical processes that evolve on them.

Mobility Network Backbones and Link Salience

A project was initiated with the goal to extract the operational backbone in complex, multi-scale mobility networks based on shortest path trees that can be defined on complex networks. All transportation and mobility networks that are employed in computational models for disease dynamics can be represented as a weighted symmetric matrix W_ij between locations i and j in which the weight quantifies the traffic of individuals between these locations. Based on the intuitive notion that effective distance is inversely proportional to traffic (the more traffic between two locations the closer they effectively are, irrespective of geographic distance), a shortest path tree of a chosen location is the defined as the collection of most effective routes to all the other locations. The backbone of a mobility network can be defined as connections that appear on the majority of shortest path tree. A key result of this study that was obtained in this WP2 activity is that this process naturally yields a parameter independent link measure we termed link salience that is typically bimodaly distributed in transportation networks which means that it can be employed to classify essential links from those that are not. A surprising corollary of this study was that these essential links are not necessarily the strongest links in the network and link salience does not correlate substantially with common link centrality measures such as weighted betweenness centrality. In a comparative analysis we investigated the worldwide air transportation network as well as a multi-scale mobility network in the US. The results of this study are currently prepared for publication.

Reducing complexity in multi-scale mobility networks. The concept of link salience permits the identification of essential links in complex, highly redundant mobility networks. The top row depict the worldwide air-transportation network (right) and a multi-scale mobility network in the United States. The bottom rows indicate the reduced networks depicting only the most essential connections which are operationally important in the spatial spread of diseases.

Tour de Sys: The Traveler’s View of a Network

Tomography is a procedure long used in the biological and physical sciences to study an object by producing images of many thin slices of it, rather than trying to study a picture of the entire object all at one. For example, the gross anatomy of organs is often illustrated using pictures of tissue slices taken at various depths, rather than trying to display a picture of the entire organ. A more general way to think about tomography is that it allows you to study a very complicated object by ignoring most of the information you have. Of course, this is done in a very structured way that depends on a well-defined parameter. In an organ tomogram, you may ignore all of the organ’s anatomy except what you find at a height of 1 mm from the bottom. The height is a parameter; by varying the height, you view a series of extremely restricted pictures that, together, allow you to build up very detailed information about the organ, information that would not be available by looking at a three-dimensional picture of the organ’s exterior. The idea of using a well-defined parameter to restrict and organize information is powerful, and we have been able to apply it to the study of networks in what we like to refer to as a novel way. In this two-minute video we explain and visualize Shortest Path Tomography, the basic idea behind this study.

SPATO – Shortest Path tree Tomography

A second project that was initiated and is intimately connected to WP4 is the development of an interactive mobility network analysis tool for the visual display of mobility networks and disease dynamical processes that evolve on them. To this end the interactive software SPATO was developed based on the technique of shortest path tree tomography. SPATO reads origin destination data that defines mobility networks, automatically computes network characterizations, modularity structures, centrality measures of interest and statistical features of a given network. The visualization algorithm of SPATO extracts mobility networks from their geographical embedding and visualizes the network based on shortest paths and effective distances. The interactive tool permits the visualization of network characteristics, node specific parameters and allows to investigate the perspective of mobility networks from a node of the user’s choice. SPATO is currently available as a testable beta version, was implemented in the open source JAVA class Processing and will be made available to the partners of the the program once a usable data interface has been implemented. The figure below illustrates screenshots of SPATO for various networks.

Multi-scale mobility networks as visualized by shortest path tree tomography. Each panel depicts screenshots of the interactive network visualization tool SPATO that was developed in WP in order to visualize disease dynamical processes on a global scale, extract generic features of the dynamic process and relate them to topological features of the underlying mobility network.

The SPATO visual explorer can be downloaded at the page: http://www.spato.net/

Theme 2. Multi-scale Community structure and Effective geographic boundaries in Europe

We finalized a project in which we used a multi scale proxy network for human mobility to compute the effective large community structure and effective boundaries. The analysis is based on network modularity maximization and uses a generalized simulated annealing algorithm. Based on this approximate technique we obtained ensembles of community partitionings of the counties in the United States and by superposition were able to determine effective boundaries in the United States. We anticipate to carry out the analogous study for a set of European countries based on the proxy network obtained from trackable items and geocaching.com.

The study was published in Thiemann C et al.,PLoS ONE 5(11): e15422.

Theme 3. Dynamics on heterogeneous networks: theoretical foundations and high performance agent based simulation

One of the key motivations in the development of shortest path tomography (SPATO) was the need to understand the complexity exhibited in spatio-temporal patterns of disease dynamics. In contemporary visualizations, disease dynamics are typically displayed geographically, i.e. a geographical projection. In these geographic representations dynamic patterns typically exhibit non-local and multi-scale fractal structure. However, contemporary models on global disease dynamics often generate patterns that share many features irrespective of the specific modeling paradigm (stochastic metapopulation models, sophisticated and detailed agent based models, etc.). The goal of this project was to investigate disease dynamics in the context of effective distances employed in the SPATO program described above. A very important insight of this project was that disease dynamics, irrespective of initial outbreak location exhibit characteristic symmetries in the effective distance representation. This is a direct consequence of the symmetries in the underlying transportation and mobility networks. Using epidemic arrival times and effective distances this approach permits the definition of effective spreading speeds despite the fact that in geographic representations a clear wave front cannot be determined when long range traffic is involved. Currently this project is being finalized and will be submitted for publication in the next few months.

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