We study the incidence rate of damped { Ly } \alpha systems associated with the host galaxies of gamma-ray bursts ( GRB-host-DLAs ) as functions of neutral hydrogen column density ( N _ { HI } ) and projected star formation rate ( SFR ) using cosmological SPH simulations .
Assuming that the occurrence of GRBs is correlated with the local SFR , we find that the median N _ { HI } of GRB-host-DLAs progressively shifts to lower N _ { HI } values with increasing redshift , and the incidence rate of GRB-host-DLAs with \log N _ { HI } > 21.0 decreases rapidly at z \geq 6 .
Our results suggest that the likelihood of observing the signature of IGM attenuation in GRB afterglows increases towards higher redshift , because it will not be blocked by the red damping wing of DLAs in the GRB host galaxies .
This enhances the prospects of using high-redshift GRBs to probe the reionization history of the Universe .
The overall incidence rate of GRB-host-DLAs decreases monotonically with increasing redshift , whereas that of QSO-DLAs increases up to z = 6 .
A measurement of the difference between the two incidence rates would enable an estimation of the value of \eta _ { GRB } , which is the mass fraction of stars that become GRBs for a given amount of star formation .
Our predictions can be tested by upcoming high- z GRB missions , including JANUS ( Joint Astrophysics Nascent Universe Scout ) and SVOM ( Space multi-band Variable Object Monitor ) .