  Direct observations of young stellar objects are important to test
established theories of planet formation. PDS 70 is one of the few cases where
robust evidence favours the presence of two planetary mass companions inside
the gap of the transition disk. Those planets are believed to be going through
the last stages of accretion from the protoplanetary disk, a process likely
mediated by a circumplanetary disk (CPD). We aim to develop a three dimensional
radiative transfer model for the dust component of the PDS 70 system which
reproduces the system's global features observed at two different wavelengths:
855 $\mu\, \mathrm{m}$ with ALMA and 1.25 $\mu\, \mathrm{m}$ with VLT/SPHERE.
We use this model to investigate the physical properties of the planetary
companion PDS 70 c and its potential circumplanetary disk. We select initial
values for the physical properties of the planet and CPD through appropriate
assumptions about the nature and evolutionary stage of the object. We modify
iteratively the properties of the protoplanetary disk until the predictions
retrieved from the model are consistent with both data sets. We provide a model
that jointly explains the global features of the PDS 70 system seen in
submillimeter and polarised-scattered light. Our model suggests that spatial
segregation of dust grains is present in the protoplanetary disk. The
submillimeter modelling of the PDS 70 c source favours the presence of an
optically thick CPD and places an upper limit to its dust mass of 0.7
$M_\oplus$. Furthermore, analysis of the thermal structure of the CPD
demonstrates that the planet luminosity is the dominant heating mechanism of
dust grains inside 0.6 au from the planet while heating by stellar photons
dominates at larger planetocentric distances.
