title: Global epidemic invasion thresholds in directed cattle subpopulation networks having source, sink, and transit nodes.
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.
authors.affiliation: USDA-ARS, Center for Grain and Animal Health Research, Arthropod Borne Animal Diseases Research Unit, 1515 College Avenue, Manhattan, KS 66502, USA. Electronic address: phillip.schumm@ars.usda.gov.
authors.forename: Phillip
authors.initials: P
authors.lastname: Schumm
authors.affiliation: Kansas State University, Electrical and Computer Engineering Department, Epicenter, USA.
authors.forename: Caterina
authors.initials: C
authors.lastname: Scoglio
authors.affiliation: Northeastern University, College of Computer and Information Science, Laboratory for the Modeling of Biological and Socio-technical Systems, USA.
authors.forename: Qian
authors.initials: Q
authors.lastname: Zhang
authors.affiliation: Istanbul Technical University, Department of Physics, Faculty of Sciences and Letters, Maslak 34469, Istanbul, Turkey.
authors.forename: Duygu
authors.initials: D
authors.lastname: Balcan
mesh_terms: D000818:Animals; D050936:Basic Reproduction Number; D002417:Cattle; D002418:Cattle Diseases / Q000453:epidemiology* / Q000635:transmission*; D003198:Computer Simulation; D058872:Epidemics; D038622:Internationality; D058751:Livestock; D008954:Models, Biological; D013269:Stochastic Processes
keywords: Infected; Recovered; Simulation; Susceptible