This paper uses the epidemic-type aftershock sequence (ETAS) point process model to study certain seismicity features of the Jiashi swarm of certain earthquakes, investigating in particular whether there is relative quiescence prior to the quite big events within the Jiashi sequence. The seven earthquake sequences studied occurred in the region of Jiashi, south of Tianshan Mountain, Xinjiang, China. The particular ETAS model that is developed is consistent with the reality of seismic activity. The various features of Jiashi swarm activity can be described as focusing in different stages. There is obvious precursory quiescence prior to most big events with Ms ≥ 6.0 within the Jiashi swarm. Thus, checking for relative quiescence can be use for earthquake prediction.