Delocalized Epidemics on Graphs: A Maximum Entropy Approach
Abstract
The susceptibleinfectedsusceptible (SIS) epidemic process on complex networks can show metastability, resembling an endemic equilibrium. In a general setting, the metastable state may involve a large portion of the network, or it can be localized on small subgraphs of the contact network. Localized infections are not interesting because a true outbreak concerns networkwide invasion of the contact graph rather than localized infection of certain sites within the contact network. Existing approaches to localization phenomenon suffer from a major drawback: they fully rely on the steadystate solution of meanfield approximate models in the neighborhood of their phase transition point, where their approximation accuracy is worst; as statistical physics tells us. We propose a dispersion entropy measure that quantifies the localization of infections in a generic contact graph. Formulating a maximum entropy problem, we find an upper bound for the dispersion entropy of the possible metastable state in the exact SIS process. As a result, we find sufficient conditions such that any initial infection over the network either dies out or reaches a localized metastable state. Unlike existing studies relying on the solution of meanfield approximate models, our investigation of epidemic localization is based on characteristics of exact SIS equations. Our proposed method offers a new paradigm in studying spreading processes over complex networks.
 Publication:

arXiv eprints
 Pub Date:
 April 2016
 arXiv:
 arXiv:1605.00198
 Bibcode:
 2016arXiv160500198D
 Keywords:

 Physics  Physics and Society;
 Computer Science  Social and Information Networks;
 Mathematics  Dynamical Systems
 EPrint:
 6 pages, 5 figures, American Control Conference2016