We provide numerical evidence for slow dynamics of the susceptible-infected-susceptible
model evolving on finite-size random networks with power-law degree distributions.
Extensive simulations were done by averaging the activity density over many realizations
of networks. We investigated the effects of outliers in both highly fluctuating (natural
cutoff) and non-fluctuating (hard cutoff) most connected vertices. Logarithmic and
power-law decays in time were found for natural and hard cutoffs, respectively. This
happens in extended regions of the control parameter space \(\lambda_1<\lambda<\lambda_2\),
suggesting Griffiths effects, induced by the topological inhomogeneities. Optimal
fluctuation theory considering sample-to-sample fluctuations of the pseudo thresholds
is presented to explain the observed slow dynamics. A quasistationary analysis shows
that response functions remain bounded at \(\lambda_2\). We argue these to be signals
of a smeared transition. However, in the thermodynamic limit the Griffiths effects
loose their relevancy and have a conventional critical point at \(\lambda_c=0\). Since
many real networks are composed by heterogeneous and weakly connected modules, the
slow dynamics found in our analysis of independent and finite networks can play an
important role for the deeper understanding of such systems.