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ARS Home » Plains Area » Manhattan, Kansas » Center for Grain and Animal Health Research » ABADRU » Research » Publications at this Location » Publication #307065
Title: Global epidemic invasion thresholds in directed cattle subpopulation networks having source, sink, and transit nodes

Author
item Schumm, Phillip
item SCOGLIO, CATERINA - Arkansas State University
item ZHANG, QIAN - Northeastern University
item BALCAN, DUYGU - Istanbul Technical University

Submitted to: Journal of Theoretical Biology
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 12/8/2014
Publication Date: 2/21/2015
Citation: Schumm, P.R., Scoglio, C.M., Zhang, Q., Balcan, D. 2015. Global epidemic invasion thresholds in directed cattle subpopulation networks having source, sink, and transit nodes. Journal of Theoretical Biology. 367: 203-221. doi:10.1016/j.jtbi.2014.12.007.

Interpretive Summary: This study considers disease spread in theoretical models of cattle movement systems. A cattle movement and demographic model simulates a large network of cattle premises and flows. When a theoretical disease is introduced into the system, it has a possibility to initialize an epidemic. We derive analytic estimations of two thresholds to define the necessary criteria for an epidemic to break out across our model system. These thresholds quantify the minimal rates of cattle movement for a model disease to (a) become an epidemic in the system and (b) spread into “last-stop” locations, such as finishing feedlots. This second threshold helps model when potentially diseased animals might be arriving at slaughterhouses and would pose a threat to food safety. We conduct several numerical experiments to explore the analytic thresholds and find a primary result suggesting that the cattle premises that serve as transit nodes for cattle are the most significant type of premises in movement-based disease control.

Technical Abstract: Through the characterization of a metapopulation cattle disease model on a directed network having source, transit, and sink nodes, we derive two global epidemic invasion thresholds. The first threshold defines the conditions necessary for an epidemic to successfully spread at the global scale. The second threshold defines the criteria that permit an epidemic to move out of the giant strongly connected component and to invade the populations of the sink nodes. As each sink node represents a final waypoint for cattle before slaughter, the existence of an epidemic among the sink nodes is a serious threat to food security. We find that the relationship between these two thresholds depends on the relative proportions of transit and sink nodes in the system and the distributions of the in-degrees of both node types. These analytic results are verified through numerical realizations of the metapopulation cattle model.