  The epidemic spreading has been studied for years by applying the mean-field
approach in both homogeneous case, where each node may get infected by an
infected neighbor with the same rate, and heterogeneous case, where the
infection rates between different pairs of nodes are different. Researchers
have discussed whether the mean-field approaches could accurately describe the
epidemic spreading for the homogeneous cases but not for the heterogeneous
cases. In this paper, we explore under what conditions the mean-field approach
could perform well when the infection rates are heterogeneous. In particular,
we employ the Susceptible-Infected-Susceptible (SIS) model and compare the
average fraction of infected nodes in the metastable state obtained by the
continuous-time simulation and the mean-field approximation. We concentrate on
an individual-based mean-field approximation called the N-intertwined Mean
Field Approximation (NIMFA), which is an advanced approach considered the
underlying network topology. Moreover, we consider not only the independent and
identically distributed (i.i.d.) infection rate but also the infection rate
correlated with the degree of the two end nodes. We conclude that NIMFA is
generally more accurate when the prevalence of the epidemic is higher. Given
the same effective infection rate, NIMFA is less accurate when the variance of
the i.i.d.\ infection rate or the correlation between the infection rate and
the nodal degree leads to a lower prevalence. Moreover, given the same actual
prevalence, NIMFA performs better in the cases: 1) when the variance of the
i.i.d.\ infection rates is smaller (while the average is unchanged); 2) when
the correlation between the infection rate and the nodal degree is positive.
