We use an efficient earthquake simulator that incorporates rate-state constitutive properties and uses boundary element method to discretize the fault surfaces,to generate the synthetic earthquakes in the fault system.Rate-and-state seismicity equation is subsequently employed to calculate the seismicity rate in a region of interest using the Coulomb stress transfer from the main shocks in the fault system. The Coulomb stress transfer is obtained by resolving the induced stresses due to the fault patch slips onto the optimal-oriented fault planes. The example results show that immediately after a main shock the aftershocks are concentrated in the vicinity of the rupture area due to positive stress transfers and then disperse away into the surrounding region toward the background rate distribution. The number of aftershocks near the rupture region is found to decay with time as Omori aftershock decay law predicts. The example results demonstrate that the rate-and-state fault system earthquakesimulator and the seismicity equations based on the ratestate friction nucleation of earthquake are well posited to characterize the aftershock distribution in regional assessments of earthquake probabilities. We use an efficient earthquake simulator that incorporates rate-state constitutive properties and uses boundary element method to discretize the fault surfaces, to generate the synthetic earthquakes in the fault system. State-and-state seismicity equation is employed employed to calculate the seismicity rate in a region of interest using the Coulomb stress transfer from the main shocks in the fault system. The Coulomb stress transfer is obtained by resolving the induced stresses due to the fault patch slips onto the optimal-oriented fault planes. a main shock the aftershocks are concentrated in the vicinity of the rupture area due to positive stress transfers and then disperse away into the surrounding region toward the background rate distribution. The number of aftershocks near the rupture region is found to decay with time as Omori aftershock decay law predicts. The example results demonstrate that the rate-and-state fault system eart hquakesimulator and the seismicity equations based on the ratestate friction nucleation of earthquake are well posited to characterize the aftershock distribution in regional assessments of earthquake probabilities.