To study the effect of metallicity on the mass-loss rate of asymptotic giant branch ( AGB ) stars , we have conducted mid-infrared photometric measurements of such stars in the Sagittarius ( Sgr dSph ) and Fornax dwarf spheroidal galaxies with the 10- \mu m camera VISIR at the VLT .
We derive mass-loss rates for 29 AGB stars in Sgr dSph and 2 in Fornax .
The dust mass-loss rates are estimated from the K - [ 9 ] and K - [ 11 ] colours .
Radiative transfer models are used to check the consistency of the method .
Published IRAS and Spitzer data confirm that the same tight correlation between K - [ 12 ] colour and dust mass-loss rates is observed for AGB stars from galaxies with different metallicities , i.e .
the Galaxy , the LMC and the SMC .

The derived dust mass-loss rates are in the range 5 \times 10 ^ { -10 } to 3 \times 10 ^ { -8 } M _ { \odot } yr ^ { -1 } for the observed AGB stars in Sgr dSph and around 5 \times 10 ^ { -9 } M _ { \odot } yr ^ { -1 } for those in Fornax ; while values obtained with the two different methods are of the same order of magnitude .
The mass-loss rates for these stars are higher than the nuclear burning rates , so they will terminate their AGB phase by the depletion of their stellar mantles before their core can grow significantly .
Some observed stars have lower mass-loss rates than the minimum value predicted by theoretical models .