Approaching the religious hierarchies and its interactions with the social hierarchies and systems through mathematical modelling can help us to understand the complexities of the socio-historical processes. In this study, a mathematical model of the power dynamics of the Discalced Carmelite religious order in early modern Goa (1610–1710) is presented. A Carmelite survival function is derived and discussed with respect to the Monarchy of Portugal and the Pope, the ones who occupied the top tier of the social and religious hierarchy with respect to the Carmelites. The application of the model correlates with the events from history as gleaned through archival sources. The study further proposes based on this model that the survival of the Carmelites in Goa could have been maximized if the proposal of Fr. Vincent de S. Francis in 1613 to station the Carmelites in Goa for the official businesses of Pope would have been accepted. This might have prevented their expulsion from Goa in 1707 by the Portuguese.