We present modeling of effective area and count rates of a TAIGA-IACT Cherenkov gamma-ray telescope unit with an upgraded camera based on semiconductor photo detectors (SiPM) OnSemi MicroFJ-60035 and optical filters SL 290‒590 and SL 280-390. In comparison with the current configuration of TAIGA-IACT where classic vacuum photomultipliers are employed, the threshold detection energy of cosmic gamma-quanta by a TAIGA-IACT unit equipped with a SIiPM-based camera and a wide-band optical filter SL 290590 would be reduced down to about 0.4 TeV, and with a narrower filter SL 280-390 down to about 0.7 TeV. Application of semiconductor photo detectors, which are stable against excess illumination, and optical filters of the near-UV band allows one to substantially increase the duty cycle of a Cherenkov gamma-ray telescopes due to the possibility to carry out observations during moonlit nights and at twilight even without a need to substantially increase the trigger threshold. Hence, one may conclude that a TAIGA-IACT unit with an upgraded camera with SiPM detectors will be an efficient instrument for studies of TeV-range emission from space gamma-ray objects.