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

Abstract

We used the movements of adult milking cows 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 cows in the Province if a reportable long-incubation infection like tuberculosis (TB) 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 cows 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 cow 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 infection chain of a farm. All four of the DHI movement networks were found to be small-world, indicating that infection 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 cow shipments and were therefore not at risk of infection from this movement network; furthermore, if infection were introduced into a DHI farm that shipped animals that year, the infection would have stopped at that farm (or at least, not been passed on by shipment of adult milking cows) >50% of the time, and 75% of the time only one more DHI farm would have become infected through animal movements. Compared to the infection 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 infection, but overestimated the lower- and upper-bound measures of potential epidemic size because it did not account for the time sequence of shipments. Our infection-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 cow movements among DHI farms. This estimate increased to 850 farms (26% of all DHI herds) if the infection were not identified for 36 months.