  It is generally accepted that scale-free networks is prone to epidemic
spreading allowing the onset of large epidemics whatever the spreading rate of
the infection. In the paper, we show that disease propagation may be suppressed
in particular fractal scale-free networks. We first study analytically the
topological characteristics of a network model and show that it is
simultaneously scale-free, highly clustered, "large-world", fractal and
disassortative. Any previous model does not have all the properties as the one
under consideration. Then, by using the renormalization group technique we
analyze the dynamic susceptible-infected-removed (SIR) model for spreading of
infections. Interestingly, we find the existence of an epidemic threshold, as
compared to the usual epidemic behavior without a finite threshold in
uncorrelated scale-free networks. This phenomenon indicates that degree
distribution of scale-free networks does not suffice to characterize the
epidemic dynamics on top of them. Our results may shed light in the
understanding of the epidemics and other spreading phenomena on real-life
networks with similar structural features as the considered model.
