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$times10^{-10}$ to 3$times10^{-8}$ M$_{odot}$yr$^{-1}$ for the observed AGB stars in Sgr dSph and around 5$times10^{-9}$ 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.
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