We develop and apply analytically tractable generative models of livestock movements at national scale. These go beyond current models through mechanistic modelling of heterogeneous trade partnership network dynamics and the trade events that occur on them. Linking resulting animal movements to disease transmission between farms yields analytical expressions for the basic reproduction number R0. We show how these novel modelling tools enable systems approaches to disease control, using R0 to explore impacts of changes in trading practices on between-farm prevalence levels. Using the Scottish cattle trade network as a case study, we show our approach captures critical complexities of real-world trade networks at the national scale for a broad range of endemic diseases. Changes in trading patterns that minimise disruption to business by maintaining in-flow of animals for each individual farm reduce R0, with the largest reductions for diseases that are most challenging to eradicate. Incentivising high-risk farms to adopt such changes exploits `scale-free' properties of the system and is likely to be particularly effective in reducing national livestock disease burden and incursion risk. Encouragingly, gains made by such targeted modifcation of trade practices scale much more favourably than comparably targeted improvements to more commonly adopted farm-level biosecurity.