Bayesian compartmental models and associated reproductive numbers for an infection with multiple transmission modes

Zoonotic visceral leishmaniasis (ZVL) is a serious neglected tropical disease that is endemic in 98 countries. ZVL is primarily transmitted via a sand fly vector. In the United States, it is enzootic in some canine populations; it is transmitted from infectious mother to pup transplacentally, and vector‐borne transmission is absent. This absence affords a unique opportunity to study (1) vertical transmission dynamics in dogs and (2) the importance of vertical transmission in maintaining an infectious reservoir in the presence of a vector. In this paper, we present Bayesian compartmental models and reproductive number formulations to examine (1) and (2), providing a mechanism to plan and evaluate interventions in regions where both transmission modes are present. First, we propose an individual‐level susceptible, infectious, removed (SIR) model to study the effect of maternal infection status during pregnancy on pup infection progression. We provide evidence that pups born to diagnostically positive mothers during pregnancy are more likely to become diagnostically positive both earlier in life, and at some point during their lifetime, than those born to diagnostically negative mothers. Second, we propose a population‐level SIR model to study the impact of a vertically maintained reservoir on propagating infection in a naive canine population through emergent vector transmission using simulation studies. We also present reproductive numbers to quantify contributions of vertically infected and vector‐infected dogs to maintaining infection in the population. We show that a vertically maintained canine reservoir can propagate infection in a theoretical naive population in the presence of a vector.