  Demographic surveys of protoplanetary disks, carried out mainly with ALMA,
have provided access to a large range of disk dust masses ($M_{\rm{dust}}$)
around stars with different stellar types and in different star-forming
regions. These surveys found a power-law relation between $M_{\rm{dust}}$ and
$M_{\star}$ that steepens in time, but which is also flatter for transition
disks (TDs). We performed dust evolution models, which included perturbations
to the gas surface density with different amplitudes to investigate the effect
of particle trapping on the $M_{\rm{dust}}-M_{\star}$ relation. These
perturbations were aimed at mimicking pressure bumps that originated from
planets. We focused on the effect caused by different stellar and disk masses
based on exoplanet statistics that demonstrate a dependence of planet mass on
stellar mass and metallicity. Models of dust evolution can reproduce the
observed $M_{\rm{dust}}-M_{\star}$ relation in different star-forming regions
when strong pressure bumps are included and when the disk mass scales with
stellar mass (case of $M_{\rm{disk}}=0.05\,M_\star$ in our models). This result
arises from dust trapping and dust growth beyond centimeter-sized grains inside
pressure bumps. However, the flatter relation of $M_{\rm{dust}}-M_{\star}$ for
TDs and disks with substructures cannot be reproduced by the models unless the
formation of boulders is inhibited inside pressure bumps. In the context of
pressure bumps originating from planets, our results agree with current
exoplanet statistics on giant planet occurrence increasing with stellar mass,
but we cannot draw a conclusion about the type of planets needed in the case of
low-mass stars. This is attributed to the fact that for $M_\star<1\,M_\odot$,
the observed $M_{\rm{dust}}$ obtained from models is very low due to the
efficient growth of dust particles beyond centimeter-sizes inside pressure
bumps.
