The foot-and-mouth disease virus (FMDV) "carrier" state was defined by van Bekkum in 1959. It was based on the recovery of infectious virus 28 days or more post infection and has been a useful construct for experimental studies. Using historic data from 1,107 cattle, collected as part of a population based study of endemic FMD in 2000, we developed a mixed effects logistic regression model to predict the probability of recovering viable FMDV by probang and culture, conditional on the animal's age and time since last reported outbreak. We constructed a second set of models to predict the probability of an animal being probang positive given its antibody response in three common non-structural protein (NSP) ELISAs and its age. We argue that, in natural ecological settings, the current definition of a "carrier" fails to capture the dynamics of either persistence of the virus (as measured by recovery using probangs) or the uncertainty in transmission from such animals that the term implies. In these respects it is not particularly useful. We therefore propose the first predictive statistical models for identifying persistently infected cattle in an endemic setting that captures some of the dynamics of the probability of persistence. Furthermore, we provide a set of predictive tools to use alongside NSP ELISAs to help target persistently infected cattle.