  The epidemic threshold of the susceptible-infected-susceptible (SIS) dynamics
on random networks having a power law degree distribution with exponent
$\gamma>3$ has been investigated using different mean-field approaches, which
predict different outcomes. We performed extensive simulations in the
quasistationary state for a comparison with these mean-field theories. We
observed concomitant multiple transitions in individual networks presenting
large gaps in the degree distribution and the obtained multiple epidemic
thresholds are well described by different mean-field theories. We observed
that the transitions involving thresholds which vanishes at the thermodynamic
limit involve localized states, in which a vanishing fraction of the network
effectively contribute to epidemic activity, whereas an endemic state, with a
finite density of infected vertices, occurs at a finite threshold. The multiple
transitions are related to the activations of distinct sub-domains of the
network, which are not directly connected.
