  We have developed a numerical galactic chemical evolution model. The model is
constructed such that the effect of a wide range of parameters can be
investigated. It takes into account results from stellar evolution models, a
differentiation between diverse types of core collapse SNe and the contribution
of AGB stars in the mass range 3-8 Msun. We consider the lifetime-dependent
yield injection into the ISM by all sources as well as dust destruction due to
SN shocks in the ISM. We ascertain the temporal progression of the dust mass,
the dust-to-gas and dust-to-metal mass ratios as well as other physical
properties of a galaxy and study their dependence on the mass of the galaxy,
the IMF, dust production efficiencies and dust destruction in the ISM. The
amount of dust and the physical properties of a galaxy strongly depend on the
initial gas mass available. Overall, while the total amount of dust produced
increases with galaxy mass, the detailed outcome depends on the SN dust
production efficiency, the IMF and the strength of dust destruction in the ISM.
Dust masses are higher for IMFs biased towards higher stellar masses, despite
the fact that these IMFs are more strongly affected by dust destruction in the
ISM. The sensitivity to the IMF increases as the mass of the galaxy decreases.
SNe are primarily responsible for a significant enrichment with dust at early
epochs (< 200 Myr). Dust production with a dominant contribution by AGB stars
is found to be insufficient to account for dust masses in excess of 10^8 Msun
within 400 Myr after starburst. We find that galaxies with initial gas masses
between 1-5 x 10^11 Msun are sufficiently massive to enable production of dust
masses >10^8 Msun. Our preferred scenario is dominated by SN dust production in
combination with top-heavy IMFs and moderate dust destruction in the ISM.
