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.
See also The Origin of Wheresgeorge Research
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 Wij 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.
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.