where d ij represents the Euclidian distance between the infected farm i and the susceptible farm j. The parameters a (kernel offset) and c (kernel power) are to be estimated. The kernel captures all forms of movement and contact between farms and as such, the use of a simple 2 parameter function is inevitably a highly simplified representation of the true complexity of inter-farm contacts. We examined other functional forms for the kernel (such as those used in some other analyses [19] ) but the resulting model fits were much poorer than found using the power-law kernel above.