Estimating potential epidemic size following introduction of a long-incubation disease in scale-free connected networks of milking- XXXX movements in Ontario, Canada.

@entity281 @entity378 @entity291
We used the movements of adult milking @entity291 among farms enrolled in the Dairy Herd Improvement (DHI) program in Ontario to explore the size of an epidemic that might result from farm-to-farm movements of @entity291 in the Province if a reportable long-incubation @entity378 ( @entity378 ) were introduced and not detected for 1-3 years after introduction. A directed network was created for each year (2004-2006) using all pairs of individual shipments, defined as the movement of one or more @entity291 on a single day, from a single source DHI farm to a single recipient DHI farm. A 3-year network was also developed that included all @entity291 shipments that took place during these 3 years. The lower and upper bounds of potential maximal epidemic size were estimated using four network-analysis measures: (1) the farm out-degree, (2) the size of the largest strong and weak components, (3) the bow-tie approach, classifying farms into six different areas of a directed network and (4) the @entity281 chain of a farm. All four of the DHI movement networks were found to be small-world, indicating that @entity281 could spread over considerable distances by shipments that linked potentially distant clusters of farms. The networks were also scale-free, indicating most farms had relatively few connections to other farms, while there were a few highly connected farms. Characterization of the yearly networks showed that 41-47% of DHI farms were not involved in any @entity291 shipments and were therefore not at risk of @entity281 from this movement network; furthermore, if @entity281 were introduced into a DHI farm that shipped animals that year, the @entity281 would have stopped at that farm (or at least, not been passed on by shipment of adult milking @entity291 ) >50% of the time, and 75% of the time only one more DHI farm would have become infected through animal movements. Compared to the @entity281 chain, which accounted for both the direction and the time sequence of shipments in the movement network, the other network-analysis measures provided biased estimates of potential epidemic size. The bow-tie approach provided a schematic representation of the level of risk of each farm in the network in spreading an @entity281 , but overestimated the lower- and upper-bound measures of potential epidemic size because it did not account for the time sequence of shipments. Our @entity281 -chain results suggest that introducing a long-incubation disease into the network of farms enrolled in the DHI program in Ontario that was not identified until 12 months after the incursion would, in a worst-case scenario, have resulted in 168 farms (representing 5% of all Ontario DHI herds) being infected as a consequence of adult @entity291 movements among DHI farms. This estimate increased to 850 farms (26% of all DHI herds) if the @entity281 were not identified for 36 months.
