Radiological dispersal devices (RDDs) have a potential to disperse radioactive aerosols into the atmosphere through explosions. Accurately estimating the respirable fraction of these aerosols through experiments presents a considerable challenge. Also, the modeling of aerosol particle evolution stemming from an RDD explosion is inherently complex, involving the interplay of various physical processes operating at different time scales. In this study, we propose a comprehensive numerical model to estimate the respirable fraction of aerosols generated during RDD explosions, integrating the thermodynamic properties of detonation products with microphysical aerosol processes. The model assumes particles are spherical and ignores charge effects. It is also assumed that the thermodynamic properties of the cloud are uniform within its volume and that thermal equilibrium exists between particles and the surrounding medium. Numerical simulations are conducted for diverse experimental scenarios, and performance of the model is assessed by comparing its predictions with experimental data pertaining to Carbon and Cobalt particles. Notably, the model predicts the average particle diameter of Carbon particles within the detonation front of TNT at 13.8 nm, closely matching the experimental observation of 13 nm (Rubtsov et al., 2019). Additionally, the model captures the peak value of the cobalt particle mass fraction distribution, approximating it to be around , in agreement with experimental findings (Di Lemma et al., 2016). These findings indicate that the proposed model is capable of predicting the behavior of both radioactive and non-radioactive aerosols. Also, this study underscores the potential of modeling approaches in addressing existing knowledge gaps related to RDDs, thereby contributing to enhanced impact assessment and management strategies for incidents involving RDDs.