Canine visceral leishmaniasis (CVL) is a fatal zoonotic disease usually found in tropical climates. In these tropical areas, the parasite responsible for CVL, Leishmania infantum, is primarily transmitted via a sand fly vector. To date, however, there has been no evidence of vector-borne transmission in the United States even though CVL is maintained in a population of Foxhounds. Rather, the primary mode of transmission in U.S. dogs appears to be vertical. It is not yet well understood how the dam's infection and overall health status impact the chance of transmission to her pups, or what the implications are for the pathogen basic reproductive number and interventions designed to decrease it. We address this gap by using Bayesian stochastic compartmental models incorporating several biologically motivated infection states, and derive an appropriate reproductive number for each. We provide a formal comparison of the candidate models using Bayes Factors, and discuss the implications for CVL control. We apply these techniques to vertical transmission data collected on Foxhounds in the United States from 2007-2017.