Complex responses to movement-based disease control: when livestock trading helps

Livestock disease controls are often linked to movements between farms, for example, via quarantine and pre- or post-movement testing. Designing effective controls, therefore, benefits from accurate assessment of herd-to-herd transmission. Household models of human infections make use of R*, the number of groups infected by an initial infected group, which is a metapopulation level analogue of the basic reproduction number R0 that provides a better characterization of disease spread in a metapopulation. However, existing approaches to calculate R* do not account for individual movements between locations which means we lack suitable tools for livestock systems. We address this gap using next-generation matrix approaches to capture movements explicitly and introduce novel tools to calculate R* in any populations coupled by individual movements. We show that depletion of infectives in the source group, which hastens its recovery, is a phenomenon with important implications for design and efficacy of movement-based controls. Underpinning our results is the observation that R* peaks at intermediate livestock movement rates. Consequently, under movement-based controls, infection could be controlled at high movement rates but persist at intermediate rates. Thus, once control schemes are present in a livestock system, a reduction in movements can counterintuitively lead to increased disease prevalence. We illustrate our results using four important livestock diseases (bovine viral diarrhoea, bovine herpes virus, Johne's disease and Escherichia coli O157) that each persist across different movement rate ranges with the consequence that a change in livestock movements could help control one disease, but exacerbate another.