  We used models of thermally-pulsing asymptotic giant branch (AGB) stars, that
also describe the dust-formation process in the wind, to interpret the
combination of near- and mid-infrared photometric data of the dwarf galaxy IC
1613. This is the first time that this approach is extended to an environment
different from the Milky Way and the Magellanic Clouds (MCs). Our analysis,
based on synthetic population techniques, shows a nice agreement between the
observations and the expected distribution of stars in the colour-magnitude
diagrams obtained with JHK and Spitzer bands. This allows a characterization of
the individual stars in the AGB sample in terms of mass, chemical composition,
and formation epoch of the progenitors. We identify the stars exhibiting the
largest degree of obscuration as carbon stars evolving through the final AGB
phases, descending from 1-1.25Msun objects of metallicity Z=0.001 and from
1.5-2.5Msun stars with Z=0.002. Oxygen-rich stars constitute the majority of
the sample (65%), mainly low mass stars (<2Msun) that produce a negligible
amount of dust (<10^{-7}Msun/yr). We predict the overall dust-production rate
from IC 1613, mostly determined by carbon stars, to be 6x10^{-7}Msun/yr with an
uncertainty of 30%. The capability of the current generation of models to
interpret the AGB population in an environment different from the MCs opens the
possibility to extend this kind of analysis to other Local Group galaxies.
