A deterministic mathematical model of the population biology of pseudorabies in swine was used to clarify some of the basic features of the host-virus relationship and to inquire into the circumstances that promote or impede virus persistence in a single herd. When the basic reproductive rate of the infection (ie, the number of secondary infections resulting from the introduction of a single infective animal into a wholly susceptible herd) is greater than unity, the model suggests that the number of infective individuals in the herd will undergo highly damped oscillations to a final equilibrium level. The most important determinants of virus persistence are herd size and the density at which sows are maintained. There is a threshold density of susceptible individuals below which the virus will eventually be eliminated from the herd, even when specific control measures are lacking. Test and removal strategies hasten virus elimination when herd density is already below threshold, but are otherwise likely to succeed only when the removal of latent infections reduces the basic reproductive rate of the infection below unity. Vaccination strategies may also result in virus elimination, but only in relatively small herds.