Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-05-09
Phys. Rev. E 82, 036115 (2010)
Physics
Condensed Matter
Statistical Mechanics
10 pages, 5 figures, 1 Appendix. Published in Phys. Rev. E (mistakes in the PRE version are corrected here)
Scientific paper
10.1103/PhysRevE.82.036115
Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently couple the dynamics of the network elements (nodes, vertices, individuals...) on the one hand and their recurrent topological patterns (subgraphs, groups...) on the other hand. In a SIS model of epidemic spread on social networks with community structure, this approach yields a set of ODEs for the time evolution of the system, as well as analytical solutions for the epidemic threshold and equilibria. The results obtained are in good agreement with numerical simulations and reproduce random networks behavior in the appropriate limits which highlights the influence of topology on the processes. Finally, it is demonstrated that our model predicts higher epidemic thresholds for clustered structures than for equivalent random topologies in the case of networks with zero degree correlation.
Allard Antoine
Dube' Louis J.
Hébert-Dufresne Laurent
Marceau Vincent
Noël Pierre-André
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