  Reckoning of pairwise dynamical correlations significantly improves the
accuracy of mean-field theories and plays an important role in the
investigation of dynamical processes on complex networks. In this work, we
perform a nonperturbative numerical analysis of the quenched mean-field theory
(QMF) and the inclusion of dynamical correlations by means of the pair quenched
mean-field (PQMF) theory for the susceptible-infected-susceptible (SIS) model
on synthetic and real networks. We show that the PQMF considerably outperforms
the standard QMF on synthetic networks of distinct levels of heterogeneity and
degree correlations, providing extremely accurate predictions when the system
is not too close to the epidemic threshold while the QMF theory deviates
substantially from simulations for networks with a degree exponent
$\gamma>2.5$. The scenario for real networks is more complicated, still with
PQMF significantly outperforming the QMF theory. However, despite of high
accuracy for most investigated networks, in a few cases PQMF deviations from
simulations are not negligible. We found correlations between accuracy and
average shortest path while other basic networks metrics seem to be
uncorrelated with the theory accuracy. Our results show the viability of the
PQMF theory to investigate the high prevalence regimes of recurrent-state
epidemic processes on networks, a regime of high applicability.
