Understanding of spatiotemporal transmission of infectious diseases has improved significantly in recent years. Advances in Bayesian inference methods for individual-level geo-located epidemiological data have enabled reconstruction of transmission trees and quantification of disease spread in space and time, while accounting for uncertainty in missing data. However, these methods have rarely been applied to endemic diseases or ones in which asymptomatic infection plays a role, for which additional estimation methods are required. Here, we develop such methods to analyze longitudinal incidence data on visceral leishmaniasis (VL) and its sequela, post-kala-azar dermal leishmaniasis (PKDL), in a highly endemic community in Bangladesh. Incorporating recent data on VL and PKDL infectiousness, we show that while VL cases drive transmission when incidence is high, the contribution of PKDL increases significantly as VL incidence declines (reaching 55% in this setting). Transmission is highly focal: 85% of mean distances from inferred infectors to their secondary VL cases were <300 m, and estimated average times from infector onset to secondary case infection were <4 mo for 88% of VL infectors, but up to 2.9 y for PKDL infectors. Estimated numbers of secondary cases per VL and PKDL case varied from 0 to 6 and were strongly correlated with the infector's duration of symptoms. Counterfactual simulations suggest that prevention of PKDL could have reduced overall VL incidence by up to 25%. These results highlight the need for prompt detection and treatment of PKDL to achieve VL elimination in the Indian subcontinent and provide quantitative estimates to guide spatiotemporally targeted interventions against VL.