Visiting Speaker
Piet Van Mieghem
Professor at the Delft University of Technology
Universal Mean-Field Framework (UMFF) for SIS epidemics on networks
Thu
Jun 15, 2017
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3:00 pm
177 Huntington Ave
11th floor
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We first deduce the exact differential equation for the SIS prevalence (i.e. the average number of infected nodes) on any network, which illustrates both the importance of the cut-set (i.e. set of infective links with one infected node) and the "local-rule, global emergent property" of the SIS/SIR class, leading to phase-transitions. A spectral decomposition of the exact time-varying prevalence leads to the "tanh-formula" for any network. I will briefly illustrate the potential of the so-called "tanh-formula".

After this introduction, we propose a new approximation framework, the Universal Mean-Field Framework (UMFF), that unifies and generalizes a number of existing mean-field approximation methods for the SIS epidemic model on complex networks. The main novelty of UMFF lies in the topological approximation of the SIS epidemic process by graph partitioning and by the famous isoperimetric inequality. These deep network concepts, related to Szemeredi’s regularity lemma, allow us to bound the approximation errors of UMFF and thus of the existing mean-field methods, like our N-Intertwined Mean-Field Approximation (NIMFA) and the Heterogeneous Mean-Field (HMF, Pastor-Satorras & Vespignani), that are particular cases of UMFF.

about the speaker
Piet Van Mieghem is professor at the Delft University of Technology with a chair in telecommunication networks and chairman of the section Network Architectures and Services (NAS) since 1998. His main research interests lie in the modelling and analysis of complex networks (such as infrastructural, biological, brain, social networks) and in new Internet-like architectures and algorithms for future communications networks.

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