Highly dynamic animal contact network and implications on disease transmission

Chen, Shi; White, Brad J.; Sanderson, Michael W.; Amrine, David E.; Ilany, Amiyaal; Lanzas, Cristina

Investigating Animal Contact Network Structure. Animal contact networks were constructed from position data recorded by a wireless remote location system in three pens of calves over 8 d (21, 21 , and 27 animals in pen #1, #2, and #3, respectively), as described in our previous study 20 (also a brief summary in SI methods), and were undirected in this study (i.e. animal i contacting animal j implied animal j contacting animal i simultaneously). All the experiments were approved by and complied with animal regulation policy of the Kansas State University. A contact was defined as whenever two animals were within a distance of 1 foot (,0.3 m, about the length of a calf head) in a fixed time interval (10 s), and if two animals were in contact for several consecutive intervals, each 10-s interval would be regarded as an individual contact. Therefore, the contact networks not only described whether two animals were in contact, but also explicitly measured how many contacts (and the total duration of contacts, since each contact lasted for a fixed 10 s) were made in each given period. In this study the total number of contacts of each individual were aggregated at an hourly level, as well as at a daily level, for comparison. Among various quantitative measurements of network structure, centrality measurements were used to differentiate relative importance of the individuals in the group [21] [22] [23] [24] . We computed degree centrality, which specifically measures the number of edges on a node (in this study, equivalent to one individual calf's total number of contacts with other animals in a 1-h period; one calf could have more than one contact with another calf in that period). The degree distributions of the contact networks at pen level (pen #1 through pen #3) and for all pens combined for the entire observation period were fitted with different probability distribution, including gamma and normal distributions with maximum likelihood methods, and the goodness of fit was determined by a two-sided Kolmogorov-Smirnov (K-S) test. Contacts were further divided on hourly bases, and the degree distribution of hourly networks was computed and compared against that of the entire observation period. The degree order, which measures the order of individual degrees in the network (lowest number corresponding to 1, highest number corresponding to the number of cattle in the pen, in ascending order), was computed for each hour and averaged over the entire period (192 h) to investigate whether certain calves were consistently more active (consistently higher degree order) in the contact network throughout the time. A hypothetical population of animals with constant hourly degree order was simulated, and the distribution of summed contact of each pen and the hypothetical population was compared by the K-S test to investigate whether the observed network order was consistent through time.