Earthquake aftershocks display spatiotemporal correlations arising from their self-organized critical behavior. Dynamic deterministic modeling of aftershock series is challenging to carry out due to both the physical complexity and uncertainties related to the different parameters which govern the system. Nevertheless, numerical simulations with the help of stochastic models such as the fiber bundle model (FBM) allow the use of an analog of the physical model that produces a statistical behavior with many similarities to real series. FBMs are simple discrete element models that can be characterized by using few parameters. In this work, the aim is to present a new model based on FBM that includes geometrical characteristics of fault systems. In our model, the faults are not described with typical geometric measures such as dip, strike, and slip, but they are incorporated as weak regions in the model domain that could increase the likelihood to generate earthquakes. In order to analyze the sensitivity of the model to input parameters, a parametric study is carried out. Our analysis focuses on aftershock statistics in space, time, and magnitude domains. Moreover, we analyzed the synthetic aftershock sequences properties assuming initial load configurations and suitable conditions to propagate the rupture. As an example case, we have modeled a set of real active faults related to the Northridge, California, earthquake sequence. We compare the simulation results to statistical characteristics from the Northridge sequence determining which range of parameters in our FBM version reproduces the main features observed in real aftershock series. From the results obtained, we observe that two parameters related to the initial load configuration are determinant in obtaining realistic seismicity characteristics: (1) parameter P, which represents the initial probability order, and (2) parameter π, which is the percentage of load distributed to the neighboring cells. The results show that in order to reproduce statistical characteristics of the real sequence, larger πfrac values (0.85<πfrac<0.95) and very low values of P (0.0