As an aid to the study of bovine tuberculosis (TB), a simple model has been developed of an epidemic involving two species, cattle and badgers. Each species may infect the other. The proportion of animals affected is assumed relatively small so that the usual nonlinear aspects of epidemic theory are avoided. The model is used to study the long-run and transient effect on cattle of culling badgers and the effect of a period without routine testing for TB, such as occurred during the 2001 epidemic of foot-and-mouth disease in Great Britain. Finally, by examining the changes in cattle TB over the last 15 years, and with some other working assumptions, it is estimated that the net reproduction number of the epidemic is Ϸ1.1. The implications for controlling the disease are discussed.animal ecology ͉ epidemiology ͉ mathematical model M athematical modeling of infectious disease, especially in humans, has a long history (1). Two very different kinds of dynamical model are simple outline and quasirealistic models. The former aim to capture the essence of a complex situation in a few key aspects and then to use these to explain the qualitative patterns of behavior to be expected and even to give semiquantitative predictions. Quasirealistic models, by contrast, aim to get much closer to reality by representing, almost inevitably in a model implemented by computer rather than by mathematical analysis, as many features of reality as is feasible. Despite the attractions of greater realism, a common problem with such models is the need to specify the values of a considerable number of forms of dependence and the numerical values of unknown parameters, often, as in the present instance, aspects about which little is known. The consequent need for extensive and systematic sensitivity analyses may undermine the usefulness of such models and mean that such data as are available are consistent with many different interpretations.In the present work we consider a deterministic multispecies transmission model of the former simpler type to describe Mycobacterium bovis infection in cattle and badgers. After setting out a fairly general model framework allowing both within-and between-species transmission, we look at a number of special situations corresponding in particular to interventions on one or other species.
General Model SpecificationWe consider a reasonably homogeneous area such that at time t there are X 1 (t) ϭ C(t) infected cattle per km 2 and X 2 (t) ϭ B(t) infected badgers per km 2 . We suppose that the proportions of infected animals are relatively small, say Ͻ0.2, so that the nonlinear effects characteristic of epidemic theory, because of the depletion of the pool of susceptible animals, are not important. This assumption seems reasonable because reports of more than a small number of reactor cattle within individual herd breakdowns are rare. Also, we do not distinguish between infected and infectious animals, thus making the approximation that all infected animals of a particular species are equally infectious.A majo...