After about five years since the first detection of a very high energy (VHE) emission component from gamma-ray bursts (GRBs), efforts in improving the follow-up observation programs on transient events by the most important VHE instruments kept growing. The need to widen the accessible observational window above the TeV band has been proven by the detection of multi-TeV signals in events such as GRB 190829A and, recently, GRB 221009A. Furthermore, the association of high-energy neutrinos and gravitational waves with astrophysical sources has opened the era of multi-messenger astrophysics, potentially providing unique insights into the physics of extreme cosmic accelerators. The ASTRI Mini-Array experiment, composed of nine imaging atmospheric dual-mirror Cherenkov telescopes, is being built at the Teide Observatory site. Although not specifically thought of as a transient facility, it might play an important role in studying the TeV component in transient sources, opening new opportunities for time-domain astrophysics. The array will be equipped with a dedicated transient handler that will allow us to perform specific follow-up campaigns on a wide range of astrophysical sources like GRBs, galactic transients, and the possible VHE electromagnetic counterpart of neutrinos and gravitational waves.
We studied the feasibility of detecting a TeV emission component from transient events such as on- and off-axis GRBs. This preliminary study explores the physical parameters space that would maximize the possibility of producing detectable TeV signatures from nearby events. The implementation and optimization of a possible ASTRI Mini-Array observational strategy based on specific science cases will also be discussed.