A deterministic mathematical model of Mycobacterium avium subsp. paratuberculosis transmission on commercial US dairy farms

摘要

Prevalence of Johne's disease on U.S. dairy farms is estimated at one-fifth of all herds, and larger herds are found to be infected more often. Despite a low prevalence of high-shedding animals, elimination of MAP from herds has proven exceptionally challenging, with few published reports of successful eradication from infected farms. Mathematical modeling may help us understand this apparent contradiction. A deterministic mathematical model of MAP transmission on commercial US dairies was developed. It builds upon and modifies the assumptions in previous work to best reflect the pathobiology of the disease. Of the animals which test positive for MAP, high levels of bacterial shedding are noted in only a small proportion. Transmission was modeled using ordinary differential equations. Calculation of transmission parameters in these models is necessarily non-linear. Previous models of infection utilized linear dynamics only and therefore lack sensitivity to changes in susceptible population size. Animal turnover rates were obtained from the literature and transition from disease states were calculated from retrospective fecal culture data from herds in New York and Pennsylvania. The model shows that aggressive test-and-cull strategies do not result in successful elimination of MAP in a short timeframe. Transmission is relatively insensitive to the presence of high shedding animals. According to the model, multiple levels of contagiousness among infected adult animals and MAP shedding by infected calves explained the maintenance of low prevalence infections in herds. Although previous experimental studies support the potential of infectious transmission among young calves, further research with natural infections is needed to verify the existence of a pool of infectious young animals. If this group of animals is diagnostically identifiable, elimination strategies may need to address this route of transmission.