Potential for transmission of infections in networks of cattle farms.

The aim of this analysis is to evaluate how generic properties of networks of livestock farms connected by movements of cattle impact on the potential for spread of infectious diseases. We focus on endemic diseases with long infectious periods in affected cattle, such as bovine tuberculosis. Livestock farm networks provide a rare example of large but fully specified directed contact networks, allowing investigations into how properties of such networks impact the potential for spread of infections within them. Here we quantify the latter in terms of the basic reproduction number, R₀, and partition the contributions to R₀ from first order moments (mean contact rates) and second order moments (variances and covariances of contact rates) of the farm contact matrices. We find that the second order properties make a substantial contribution to the magnitude of R₀ similarly to that reported for other populations. Importantly, however, we find that the magnitude of these effects depends on exactly how the contacts between farms are defined or weighted. We note that the second order properties of a directed contact network may vary through time even with little change in the mean contact rates or in overall connectedness of the network.