Dynamic Communicability Predicts Infectiousness
Using real, time-dependent social interaction data, we look at correlations between some recently proposed dynamic centrality measures and summaries from large-scale epidemic simulations. The evolving network arises from email exchanges. The centrality me
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Abstract Using real, time-dependent social interaction data, we look at correlations between some recently proposed dynamic centrality measures and summaries from large-scale epidemic simulations. The evolving network arises from email exchanges. The centrality measures, which are relatively inexpensive to compute, assign rankings to individual nodes based on their ability to broadcast information over the dynamic topology. We compare these with node rankings based on infectiousness that arise when a full stochastic SI simulation is performed over the dynamic network. More precisely, we look at the proportion of the network that a node is able to infect over a fixed time period, and the length of time that it takes for a node to infect half the network. We find that the dynamic centrality measures are an excellent, and inexpensive, proxy for the full simulation-based measures.
1 Background and Motivation In many social interactions, the timing of the connections is vital. Suppose A meets B today and B meets C tomorrow. This makes it possible for a message, or a disease, to pass from A to B, but not from C to A. Further, the more active B happens to be tomorrow, the more potential there is for today’s A–B link to have a downstream effect. Several authors have pointed out the need to account for topological dynamics when considering disease propagation. The work in [15] considers the stages that sexually transmitted diseases (STDs) pass through when infecting subpopulations of a network, and shows that the timing in the connectivity between individuals plays a crucial role. In [10] a disease is simulated with an SI model (as we use here) and an SIR alternative, over contact networks relating to high-end prostitution. Both a static and a temporal view of the A.V. Mantzaris () D.J. Higham Department of Mathematics and Statistics, University of Strathclyde, Glasgow, UK e-mail: [email protected] P. Holme and J. Saram¨aki (eds.), Temporal Networks, Understanding Complex Systems, DOI 10.1007/978-3-642-36461-7 14, © Springer-Verlag Berlin Heidelberg 2013
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interaction data is used, and the results show that temporal effects play a key role. Epidemic simulations over temporal connectivity data are also used in [7] to explore vaccination strategies. Similarly, the spread of computer malware over temporal networks is considered in [13, 14], and strategies developed for the immunisation of key nodes. The SI framework is used in [2] to characterise the global structure of a temporal network. From a network science perspective, it is natural to seek generic centrality measures that rank individual nodes according to their “importance.” In the case of static network topology, there is a wealth of such measures, most of which can be traced back to the social network analysis community [4]. Devising centrality measures that apply to time-dependent networks is a more recent pursuit. The work of [12] used a shortest-path-counting approach to measure the closeness/betweeness
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