Physics – Physics and Society
Scientific paper
2011-05-27
Physics
Physics and Society
24 pages, 7 figures
Scientific paper
In stark contrast to previous common wisdom that epidemic activity and thresholds in heterogeneous networks are dominated by the elements with the largest number of connections (the hubs), recent research has pointed out the role of the most efficient spreaders, located at the innermost, dense core of the network, in sustaining epidemic processes. Here we show that the mechanism responsible of epidemic spreading depends on the dynamical pattern of the epidemic process. For epidemics with a transient state, activity is essentially boosted by the innermost core of the network. On the contrary, epidemics allowing a steady state present a dual scenario, where either the vertex with the largest connectivity independently sustains activity and propagates it to the rest of the system, or, alternatively, the innermost core of the network collectively turns into the active state, maintaining it on a global scale. Which one of these two mechanisms actually governs the dynamics depends on the network features. In uncorrelated networks the former dominates if the degree distribution decays with an exponent larger than 5/2, and the latter otherwise. Topological correlations, rife in real complex networks, may however strongly perturb this picture, enhancing or suppressing the relative importance of the two mechanisms.
Castellano Claudio
Pastor-Satorras Romualdo
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