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 , \alpha -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 \sim 5 , whereas in the case of strong number density evolution it increases slightly from z=10 to z \sim 2 and then it decreases down to z=0 .
Finally , we found tha the total cosmic dust mass density at the present time is : \Omega _ { dust } \sim 3.5 \cdot 10 ^ { -5 } in the case of pure luminosity evolution and \Omega _ { dust } \sim 7 \cdot 10 ^ { -5 } in the case of number density evolution .