  In this work, we present results that simultaneously constrain the dust size
distribution, dust-to-gas ratio, fraction of dust re-deposition, and total mass
production rates for comet 67P/Churyumov-Gerasimenko. We use a 3D Direct
Simulation Monte Carlo (DSMC) gas dynamics code to simulate the inner gas coma
of the comet for the duration of the Rosetta mission. The gas model is
constrained by ROSINA/COPS data. Further, we simulate for different epochs the
inner dust coma using a 3D dust dynamics code including gas drag and the
nucleus' gravity. Using advanced dust scattering properties these results are
used to produce synthetic images that can be compared to the OSIRIS data set.
These simulations allow us to constrain the properties of the dust coma and the
total gas and dust production rates. We determined a total volatile mass loss
of $(6.1 \pm 1.5) \cdot 10^9$~kg during the 2015 apparition. Further, we found
that power-laws with $q=3.7^{+0.57}_{-0.078}$ are consistent with the data.
This results in a total of $5.1^{+6.0}_{-4.9}\cdot10^9$~kg of dust being
ejected from the nucleus surface, of which $4.4^{+4.9}_{-4.2}\cdot10^9$~kg
escape to space and $6.8^{+11}_{-6.8}\cdot10^8$~kg (or an equivalent of
$14^{+22}_{-14}$~cm over the smooth regions) is re-deposited on the surface.
This leads to a dust-to-gas ratio of $0.73^{+1.3}_{-0.70}$ for the escaping
material and $0.84^{+1.6}_{-0.81}$ for the ejected material. We have further
found that the smallest dust size must be strictly smaller than $\sim30\mu$m
and nominally even smaller than $\sim12\mu$m.
