The nature of some GRB host galaxies has been investigated by means of chemical evolution models of galaxies of different morphological type following the evolution of the abundances of H, He, C, N, O, $α$-elements, Ni, Fe, Zn, and including also the evolution of dust. By comparing predictions with abundance data, we were able to constrain nature and age of GRB hosts. We also computed a theoretical cosmic dust rate, including stellar dust production, accretion and destruction, under the hypotheses of pure luminosity evolution and strong number density evolution of galaxies. We suggest that one of the three GRB hosts is a massive proto-spheroid catched during its formation, while for the other two the situation is more uncertain, although one could perhaps be a spheroid and the other a spiral galaxy. We estimated the chemical ages of the host galaxies which vary from 15 to 320 Myr. Concerning the cosmic effective dust production rate in an unitary volume of the Universe, our results show that in the case of pure luminosity evolution there is a first peak between redshift $z=8$ and $9$ and another at $z∼ 5$, whereas in the case of strong number density evolution it increases slightly from $z=10$ to $z∼ 2$ and then it decreases down to $z=0$. Finally, we found tha the total cosmic dust mass density at the present time is: $Ω_{dust} ∼ 3.5⋅ 10^{-5}$in the case of pure luminosity evolution and $Ω_{dust} ∼ 7⋅ 10^{-5}$ in the case of number density evolution. ; Comment: 15 pages, 10 figures, accepted for publication in MNRAS