Multiple phase transitions of the susceptible-infected-susceptible epidemic model on complex networks

摘要

The epidemic threshold of the susceptible-infected-susceptible (SIS) dynamicson random networks having a power law degree distribution with exponent$\gamma>3$ has been investigated using different mean-field approaches, whichpredict different outcomes. We performed extensive simulations in thequasistationary state for a comparison with these mean-field theories. Weobserved concomitant multiple transitions in individual networks presentinglarge gaps in the degree distribution and the obtained multiple epidemicthresholds are well described by different mean-field theories. We observedthat the transitions involving thresholds which vanishes at the thermodynamiclimit involve localized states, in which a vanishing fraction of the networkeffectively contribute to epidemic activity, whereas an endemic state, with afinite density of infected vertices, occurs at a finite threshold. The multipletransitions are related to the activations of distinct sub-domains of thenetwork, which are not directly connected.