We identify the nature of high-redshift long gamma-ray burst (LGRB) host galaxies by comparing the observed abundance ratios in the interstellar medium with detailed chemical evolution models accounting for the presence of dust. We compare abundance data from LGRB afterglow spectra to abundance patterns as predicted by our models for different galaxy types. We analyze [X/Fe] abundance ratios (where X is C, N, O, Mg, Si, S, Ni, Zn) as functions of [Fe/H]. Different galaxies (irregulars, spirals, spheroids) are, in fact, characterized by different star formation histories, which produce different [X/Fe] versus [Fe/H] relations ("time-delay model"). This allows us to identify the star formation history of the host galaxies and to infer their age (i.e., the time elapsed from the beginning of star formation) at the time of the GRB events. Unlike previous works, we use newer models in which we adopt updated stellar yields and prescriptions for dust production, accretion, and destruction. We consider a sample of seven LGRB host galaxies. Our results suggest that two of them (GRB 050820, GRB 120815A) are star-forming spheroids, two (GRB 081008, GRB 161023A) are spirals, and three (GRB 090926A, GRB 050730, GRB 120327A) are irregulars. The inferred ages of the considered host galaxies span from 10 Myr to slightly more than 1 Gyr.
