Is R(0) a good predictor of final epidemic size: foot-and-mouth disease in the UK.

One of the main uses of an epidemic model is to predict the scale of an outbreak from the first few cases. In a homogeneous and non-spatial model there is a straightforward relationship between the basic reproductive ratio, R(0), and the final epidemic size; however when there is a significant spatial component to disease spread and the population is heterogeneous predicting how the epidemic size varies with the initial source of infection is far more complex. Here we use a well-developed spatio-temporal model of the spread of foot-and-mouth disease, parameterized to match the 2001 UK outbreak, to address the relationship between the scale of the epidemic and the nature of the initially infected farm. We show that there is considerable heterogeneity in both the likelihood of a epidemic and the epidemic impact (total number of farms losing livestock to either infection or control) and that these two elements are best captured by measurements at different spatial scales. The likelihood of an epidemic can be predicted from a knowledge of the reproduction ratio of the initial farm (R(i)), whereas the epidemic impact conditional on an epidemic occurring is best predicted by averaging the second-generation reproduction ratio (R(i)((2))) in a 58 km ring around the infected farm. Combining these two predictions provides a good assessment of both the local and larger-scale heterogeneities present in this complex system.