We develop and apply analytically tractable generativemodels of livestock movements at national scale. These gobeyond current models through mechanistic modelling ofheterogeneous trade partnership network dynamics and thetrade events that occur on them. Linking resulting animalmovements to disease transmission between farms yieldsanalytical expressions for the basic reproduction number R0.We show how these novel modelling tools enable systemsapproaches to disease control, using R0 to explore impacts ofchanges in trading practices on between-farm prevalencelevels. Using the Scottish cattle trade network as a case study,we show our approach captures critical complexities of realworld trade networks at the national scale for a broad rangeof endemic diseases. Changes in trading patterns thatminimize disruption to business by maintaining in-flow ofanimals for each individual farm reduce R0, with the largestreductions for diseases that are most challenging to eradicate.Incentivizing high-risk farms to adopt such changes exploits‘scale-free’ properties of the system and is likely to beparticularly effective in reducing national livestock diseaseburden and incursion risk. Encouragingly, gains made bysuch targeted modification of trade practices scale muchmore favourably than comparably targeted improvements tomore commonly adopted farm-level biosecurity.