We try to identify the nature of high redshift long Gamma-Ray Bursts (LGRBs) host galaxies by comparing the observed abundance ratios in the interstellar medium with detailed chemical evolution models accounting for the presence of dust. We compared measured abundance data from LGRB afterglow spectra to abundance patterns as predicted by our models for different galaxy types. We analysed in particular [X/Fe] abundance ratios (where X is C, N, O, Mg, Si, S, Ni, Zn) as functions of [Fe/H]. Different galaxies (irregulars, spirals, ellipticals) are, in fact, characterised by different star formation histories, which produce different [X/Fe] ratios (time-delay model). This allows us to identify the morphology of the hosts and to infer their age (i.e. the time elapsed from the beginning of star formation) at the time of the GRB events, as well as other important parameters. Relative to previous works, we use newer models in which we adopt updated stellar yields and prescriptions for dust production, accretion and destruction. We have considered a sample of seven LGRB host galaxies. Our results have suggested that two of them (GRB 050820, GRB 120815A) are ellipticals, two (GRB 081008, GRB 161023A) are spirals and three (GRB 050730, GRB 090926A, GRB 120327A) are irregulars. We also found that in some cases changing the initial mass function can give better agreement with the observed data. The calculated ages of the host galaxies span from the order of 10 Myr to little more than 1 Gyr.
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