Real-life situations showed damage effects on non-targeted cells located in the vicinity of an irradiation region, due to danger signal molecules released by the targeted cells. This effect is widely known as radiation-induced bystander effects (RIBE). The purpose of this paper is to model the interaction of non-targeted cells towards bystander factors released by the irradiated cells by using a system of structured ordinary differential equations. The mathematical model and its simulations are presented in this paper. In the model, the cells are grouped based on the number of double-strand breaks (DSBs) and mis-repair DSBs because the DSBs are formed in non-targeted cells. After performing the model's simulations, the analysis continued with sensitivity analysis. Sensitivity analysis will determine which parameter in the model is the most sensitive to the survival fraction of non-targeted cells. The proposed mathematical model can explain the survival fraction of non-targeted cells affected by the bystander factors.