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Center for Nonlinear Studies |
Studying the spread of epidemics on scale-free networks is a useful tool in understanding the behavior of real life epidemics, whether they be the spread of human diseases, or computer/email viruses. In these networks, the overlay topology (or connectivity graph) is crucial in determining the behavior of the spread of an epidemic, including defining the epidemic threshold, a value above which the disease spreads and becomes endemic. In scale-free networks with degree exponent <=3, the value of the epidemic threshold vanishes in the limit of infinite (or very large) systems, due to the presence of "hubs". Yet for real-life systems there is a finite limit, not only to the number of nodes, but for the number of connections each node can acquire. It is therefore worthwhile to study systems with an imposed hard cutoff for the number of connections each node can have. We investigate the spread of epidemics on such scale-free topologies with hard cutoffs (i.e. there are not any major hubs) and the effect of these hard cutoffs on the epidemic threshold using an SIS (Susceptible-Infected-Susceptible) model of epidemics. We find that for small values of the cutoff (relative to the network size), the value of the epidemic threshold increases significantly, most likely due to the restriction in the formation of hubs.
Host: Hasan Guclu