We developed a series of deterministic mathematical models of Mycobacterium avium subsp. paratuberculosis (MAP) transmission on commercial US dairies. Our models build upon and modify models and assumptions in previous work to better reflect the pathobiology of the disease. Parameter values were obtained from literature for animal turnover in US dairy herds and rates of transition between disease states. The models developed were used to test three hypotheses. (1) Infectious transmission following intervention is relatively insensitive to the presence of high-shedding animals. (2) Vertical and pseudo-vertical transmission increases prevalence of disease but is insufficient to explain persistence following intervention. (3) Transiently shedding young animals might aid persistence. Our simulations indicated that multiple levels of contagiousness among infected adult animals in combination with vertical transmission and MAP shedding in infected young animals explained the maintenance of low-prevalence infections in herds. High relative contagiousness of high-shedding adult animals resulted in these animals serving as the predominant contributor to transmission. This caused elimination of infection in herds using the test-and-cull intervention tested in these simulations. Addition of vertical transmission caused persistence of infection in a moderately complicated model. In the most complex model that allowed age-based contacts, calf-to-calf transmission was required for persistence.