  I extend a previous work to Susceptible-Infected-Susceptible (SIS) models on
weighted Barab\'asi-Albert scale-free networks. Numerical evidence is provided
that phases with slow, power-law dynamics emerge as the consequence of quenched
disorder and tree topologies studied previously with the Contact Process. I
compare simulation results with spectral analysis of the networks and show that
the quenched mean-field (QMF) approximation provides a reliable, relatively
fast method to explore activity clustering. This suggests that QMF can be used
for describing rare-region effects due to network inhomogeneities. Finite size
study of the QMF shows the expected disappearance of the epidemic threshold
$\lambda_c$ in the thermodynamic limit and an inverse participation ratio $\sim
0.25$, meaning localization in case of disassortative weight scheme. Contrary,
for the multiplicative weights and the unweighted trees this value vanishes in
the thermodynamic limit, suggesting only weak rare region effects in agreement
with the dynamical simulations. Strong corrections to the mean-field behavior
in case of disassortative weights explains the concave shape of the order
parameter $\rho(\lambda)$ at the transition point. Application of this method
to other models may reveal interesting rare-region effects, Griffiths Phases as
the consequence of quenched topological heterogeneities.
