A genetic epidemiological model to describe resistance to an endemic bacterial disease in livestock: application to footrot in sheep

Preventive measures and lost production due to endemic disease form an important component of the costs of production in many livestock production systems [1], and they also affect animal welfare and marketability of breeding stock. It is well known that, for many diseases, resistance has a genetic component [2] and selection for disease resistance has long been considered a promising way to reduce disease prevalence e.g. [3].Selection for resistance to an infectious disease has the added benefit that it may reduce the pathogen burden, especially when the population under selection is the main reservoir of pathogens. This will lead to an additional reduction in prevalence, in addition to the direct genetic effect, as a result of reduced contamination from infectious animals, e.g. [4].The phenotype used in selection for disease resistance is often a score, which includes a class of healthy animals, and one or more classes of affected animals. In the case of endemic diseases the vast majority of animals at any one time may be classified as healthy, and this limits the opportunity for intense selection. In a threshold model, that is appropriate for this type of data, prevalences that are much lower than 50% also lead to low heritabilities on the observed scale. A successful selection programme can therefore be expected to decrease the subsequent response to selection through increased resistance and decreased pathogen burden.Anderson and May [5] describe the spread of a microparasitic (viral or bacterial) infection through a population of animals using a so-called SIR model, based on the rates at which susceptible (S) animals are infected (I) and then recover or are removed (R). A key parameter is R0, which is the number of secondary infections caused by the first infected animal. One or more of these rates can be under genetic control and hence affect R0. This model can be extended in various ways; for instance Bishop and MacKenzie [6] have described how a disease tha