Detonators are explosive devices used for the initiation of secondary explosives in commercial and military applications. They are characterized by their initiating capability which is a critical factor for their safe and effective use but challenging to assess accurately. In this two-part study, we employ numerical simulations to investigate the blast wave generated by detonators and examine their initiating capability. The first part follows the European underwater test which evaluates detonators in isolation (direct method). The second part, presented here, investigates detonators placed within a receiving explosive charge (indirect method). Specifically, the detonator is placed inside a booster device which contains secondary explosive and together form an initiating system used to ignite mining blastholes.The physical system is modeled using a multiphysics methodology to accurately capture the response of the materials present in the configuration (explosives, metals and fluids). The reactive model is extended to account for shock desensitization where explosives become more difficult to initiate after the passage of weak shock waves. The variability of the blast wave generated by detonators, observed in the first part of the study, can lead to partial desensitization resulting in pockets of unreacted explosive which inhibit booster initiation and performance. The computational implementation is extensively validated and calibrated against experiment before employed for the study of booster initiation by a range of detonators. Results show that the booster is susceptible to shock desensitization which occurs in varying degrees for different types of detonators and can significantly impact the performance of the initiating system.