Figure 1.

Schematic of stochastic metapopulation of transmission of sheep scab within and between farms. Within a farm (black circles), there are sheep which are susceptible (S), infected (I) or carriers (C) that can move between these states in the directions indicated by the block white arrows and at the rates defined in Table 1. There is an environmental compartment (e) within each farm which has an infectious pressure determined by shedding of P. ovis mites by infected or carrier sheep within the same flock or from infected and carrier sheep from contiguous (geographically close) flocks (represented by the white and yellow dashed arrows, respectively). A farm was considered to be geographically close if it was within a 2 km radius (Table 1). Susceptible sheep become infected via transmission from the environmental compartment. Equation (1) describes the rate of change of the environmental infectious pressure over time. Sheep scab transmission between farms that are not contiguous can occur via long distance movements of sheep (orange dotted and dashed arrows) where sheep in the movement batch are infected or carriers.