title: On the robustness of in- and out-components in a temporal network.
abstract: BACKGROUND
  Many networks exhibit time-dependent topologies, where an edge only exists during a certain period of time. The first measurements of such networks are very recent so that a profound theoretical understanding is still lacking. In this work, we focus on the propagation properties of infectious diseases in time-dependent networks. In particular, we analyze a dataset containing livestock trade movements. The corresponding networks are known to be a major route for the spread of animal diseases. In this context chronology is crucial. A disease can only spread if the temporal sequence of trade contacts forms a chain of causality. Therefore, the identification of relevant nodes under time-varying network topologies is of great interest for the implementation of counteractions.
  
  
  RESULTS
  We find that a time-aggregated approach might fail to identify epidemiologically relevant nodes. Hence, we explore the adaptability of the concept of centrality of nodes to temporal networks using a data-driven approach on the example of animal trade. We utilize the size of the in- and out-component of nodes as centrality measures. Both measures are refined to gain full awareness of the time-dependent topology and finite infectious periods. We show that the size of the components exhibit strong temporal heterogeneities. In particular, we find that the size of the components is overestimated in time-aggregated networks. For disease control, however, a risk assessment independent of time and specific disease properties is usually favored. We therefore explore the disease parameter range, in which a time-independent identification of central nodes remains possible.
  
  
  CONCLUSIONS
  We find a ranking of nodes according to their component sizes reasonably stable for a wide range of infectious periods. Samples based on this ranking are robust enough against varying disease parameters and hence are promising tools for disease control.
authors: Institut für Epidemiologie, Friedrich-Loeffler-Institut, Wusterhausen, Germany.
authors: Mario
authors: M
authors: Konschake
authors: Hartmut H K
authors: HH
authors: Lentz
authors: Franz J
authors: FJ
authors: Conraths
authors: Philipp
authors: P
authors: Hövel
authors: Thomas
authors: T
authors: Selhorst
mesh_terms: D000820:Animal Diseases / Q000453:epidemiology*; D000818:Animals; D003141:Communicable Diseases / Q000453:epidemiology*; D004812:Epidemiologic Methods; D013997:Time Factors
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Feb;85(2 Pt 2):026107
references: 22463279
references: PLoS Comput Biol. 2011 Mar;7(3):e1001109
references: 21445228
references: Phys Rev Lett. 2013 Mar 15;110(11):118701
references: 25166583
references: Interdiscip Perspect Infect Dis. 2011;2011:284909
references: 21437001
references: Transbound Emerg Dis. 2008 Dec;55(9-10):382-92
references: 18840200
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Feb;83(2 Pt 2):025102
references: 21405879
references: J R Soc Interface. 2007 Aug 22;4(15):669-74
references: 17284415
references: Prev Vet Med. 2011 Feb 1;98(2-3):111-8
references: 21159393
references: Phys Rev Lett. 2007 Apr 13;98(15):158702
references: 17501392
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2010 May;81(5 Pt 2):055101
references: 20866285
references: Vet Microbiol. 2000 Nov 15;77(1-2):29-41
references: 11042398
references: Chaos. 2012 Jun;22(2):023101
references: 22757508
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jul;84(1 Pt 2):016105
references: 21867255
references: Prev Vet Med. 2009 Dec 1;92(4):341-50
references: 19775765
references: Transbound Emerg Dis. 2009 Apr;56(3):73-85
references: 19267879
references: J R Soc Interface. 2006 Oct 22;3(10):669-77
references: 16971335
references: Proc Biol Sci. 2009 Feb 7;276(1656):469-76
references: 18854300
references: J Urban Health. 2001 Sep;78(3):446-57
references: 11564848
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Aug;64(2 Pt 2):025101
references: 11497638
references: Proc Biol Sci. 2006 Nov 7;273(1602):2729-35
references: 17015320
references: PLoS One. 2012;7(5):e36439
references: 22586472
references: Prev Vet Med. 2011 May 1;99(2-4):78-90
references: 21288583
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 2):066111
references: 23005166
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Apr;83(4 Pt 2):046120
references: 21599253
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Apr;71(4 Pt 2):046119
references: 15903738
references: Phys Rev Lett. 2003 Dec 12;91(24):247901
references: 14683159
references: BMC Med. 2011 Jul 19;9:87
references: 21771290
references: PLoS One. 2011;6(5):e19869
references: 21625633
references: Prev Vet Med. 2007 Jul 16;80(2-3):143-65
references: 17383759
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Apr;83(4 Pt 2):045102
references: 21599228
references: Proc Biol Sci. 2006 Aug 22;273(1597):1999-2007
references: 16846906
references: J R Soc Interface. 2012 Nov 7;9(76):2814-25
references: 22728387
references: Transbound Emerg Dis. 2009 May;56(4):109-20
references: 19341388