Comparing Network Analysis Measures to Determine Potential Epidemic Size of Highly Contagious Exotic Diseases in Fragmented Monthly Networks of Dairy Cattle Movements in Ontario, Canada

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Abstract
Adult milking cow movements occurring in monthly periods in 2004-2006 were analysed to compare three network analysis measures to determine the lower and upper bounds of potential maximal epidemic size in an unrestrained epidemic: the out-degree, the infection chain or output domain of a farm, and the size of the strong and weak components. The directed networks generated by the movements of adult milking cows were highly fragmented. When all the farms that were not involved in shipments were included in the analysis, the risk of infection transmission through movements of adult cows was very low. To determine the size of an epidemic when an infected farm shipped cows in such a fragmented network, farm out-degree and infection chain provided similar and more reasonable estimates of potential maximal epidemic size than the size of the strong and weak components. Component analysis always provided estimates that were two to three times larger than the out-degree of infection chain approaches. For example, the upper bound was estimated to be 12-13 farms using out-degree and 16-17 farms using the infection chain, the components approach showed a range of 39-51 potentially exposed farms. Strong components provided an inflated measure of the lower bound of potential maximal epidemic size at first diagnosis because the time sequence of shipments was not considered. Weak components provided an inflated measure of the upper bound because both the time sequence and directionality of shipments between farms were ignored. Farm degree and infection chain measures should now be tested to determine their usefulness for estimating maximum epidemic size in large connected networks.

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