Advertisement

Networks and Spatial Economics

, Volume 17, Issue 4, pp 1137–1159 | Cite as

Identifying Critical Components of a Public Transit System for Outbreak Control

  • András Bóta
  • Lauren M. Gardner
  • Alireza Khani
Article

Abstract

Modern public transport networks provide an efficient medium for the spread of infectious diseases within a region. The ability to identify components of the public transit system most likely to be carrying infected individuals during an outbreak is critical for public health authorities to be able to plan for outbreaks, and control their spread. In this study we propose a novel network structure, denoted as the vehicle trip network, to capture the dynamic public transit ridership patterns in a compact form, and illustrate how it can be used for efficient detection of the high risk network components. We evaluate a range of network-based statistics for the vehicle trip network, and validate their ability to identify the routes and individual vehicles most likely to spread infection using simulated epidemic scenarios. A variety of outbreak scenarios are simulated, which vary by their set of initially infected individuals and disease parameters. Results from a case study using the public transit network from Twin Cities, MN are presented. The results indicate that the set of transit vehicle trips at highest risk of infection can be efficiently identified, and are relatively robust to the initial conditions of the outbreak. Furthermore, the methods are illustrated to be robust to two types of data uncertainty, those being passenger infection levels and travel patterns of the passengers.

Keywords

Network modeling Public transportation Infection models Outbreak control Public health 

Notes

Acknowledgements

We thank the National Health and Medical Research Council (NHMRC) for funding, project grant (No. APP1082524). The contents of the published material are solely the responsibility of the Administering Institution, a Participating Institution or individual authors and do not reflect the views of the NHMRC.

References

  1. Albert R, Barabási A (2002) Statistical mechanics of complex networks. Rev Mod Phys 74(1):47CrossRefGoogle Scholar
  2. Anderson RM, May RM (1991) Infectious diseases of humans: dynamics and control. Oxford University Press, OxfordGoogle Scholar
  3. Balcan D (2009) Multiscale mobility networks and the spatial spreading of infectious diseases. Proc Natl Acad Sci USA 106:21,484–21,489CrossRefGoogle Scholar
  4. Bóta A, Krész M, Pluhár A (2013) Approximations of the generalized cascade model. Acta Cybern 21(1):37–51CrossRefGoogle Scholar
  5. Bóta A, Gardner L, Khani A (2017) Modeling the spread of infection in public transit networks: a decision-support tool for outbreak planning and control. In: Transportation research board 96th annual meetingGoogle Scholar
  6. Brockmann D, Hufnagel L, Geisel T (2006) The scaling laws of human travel. Nature 439:462–465CrossRefGoogle Scholar
  7. Cahill E, Crandall R, Rude L, Sullivan A (2005) Space-time inuenza model with demographic, mobility, and vaccine parameters. In: Proceedings of 5th annual Hawaii international conference of mathematics statistics and related fieldsGoogle Scholar
  8. Candia J, González MC, Wang P, Schoenharl T, Madey G, Barabási A (2008) Uncovering individual and collective human dynamics from mobile phone records. J Phys A Math Theor 41(224015):11Google Scholar
  9. Carley K, Fridsma D, Casman E, Yahja A, Altman N, Chen L, Kaminsky B, Nave D (2006) Biowar: scalable agent-based model of bioattacks. IEEE Trans Syst Man Cybern Part A Syst Hum 36(2): 252–265CrossRefGoogle Scholar
  10. Cattuto C (2010) Dynamics of person-to-person interactions from distributed rfid sensor networks. PloS One 5:e11,596CrossRefGoogle Scholar
  11. Chen N, Gardner L, Rey D (2016) A bi-level optimization model for the development of real-time strategies to minimize epidemic spreading risk in air traffic networks. Transp Res Rec: J Transp Res Board No 2569Google Scholar
  12. Christakis NA, Fowler JH (2010) Social network sensors for early detection of contagious outbreaks. PLoS One 5:e12,948CrossRefGoogle Scholar
  13. Coleman J, Menzel H, Katz E (1996) Medical innovations: a diffusion study. Bobbs Merrill, New YorkGoogle Scholar
  14. De Montjoye YA, Hidalgo CA, Verleysen M, Blondel VD (2013) Unique in the crowd: The privacy bounds of human mobility. Sci Rep 3:1376CrossRefGoogle Scholar
  15. Dibble C, Feldman PG (2004) The geograph 3d computational laboratory: network and terrain landscapes for repast. J Artif Soc Soc Simul 7(1)Google Scholar
  16. Dunham J (2005) An agent-based spatially explicit epidemiological model in mason. J Artif Soc Socx Simul 9(1):3Google Scholar
  17. Ekici A, Keskinocak P, Swann J (2008) Pandemic influenza response. In: Winter simulation conference, pp 1592–1600Google Scholar
  18. Epstein JM, Cummings DAT, Chakravarty S, Singa RM, Burke DS (2002) Toward a containment strategy for smallpox bioterror: an individual-based computational approach. Brook Inst Press 2004:55Google Scholar
  19. Erath A, Löchl M, Axhausen KW (2009) Graph-theoretical analysis of the Swiss road and railway networks over time. Netw Spat Econ 9(3):379–400CrossRefGoogle Scholar
  20. Eubank S (2004) Modelling disease outbreaks in realistic urban social networks. Nature 429:180–184CrossRefGoogle Scholar
  21. Fajardo D, Gardner L (2013) Inferring contagion patterns in social contact networks with limited infection data. Netw Spat Econ 13(4):399–426CrossRefGoogle Scholar
  22. Ferguson NM (2005) Strategies for containing an emerging influenza pandemic in Southeast Asia. Nature 437:209–214CrossRefGoogle Scholar
  23. Funk S, Salathé M, Jansen VAA (2010) Modelling the influence of human behaviour on the spread of infectious diseases: a review. J R Soc Interface 7:1247–1256CrossRefGoogle Scholar
  24. Galvani AP, May RM (2005) Epidemiology: dimensions of superspreading. Nature 438:293–295CrossRefGoogle Scholar
  25. Gardner L, Sarkar S (2013) A global airport-based risk model for the spread of dengue infection via the air transport network. PLoS One 8(8):e72,129. doi: 10.1371/journal.pone.0072129 CrossRefGoogle Scholar
  26. Gardner L, Fajardo D, Waller S (2012) Inferring infection-spreading links in an air traffic network. Transp Res Rec: J Transp Res Board 2300:13–21Google Scholar
  27. Gardner L, Fajardo D, Waller S, Wang O, Sarkar S (2012) A predictive spatial model to quantify the risk of air-travel-associated dengue importation into the United States and Europe. J Trop Med 2012:103,679. doi: 10.1155/2012/103679 CrossRefGoogle Scholar
  28. Gardner L, Fajardo D, Waller S (2014) Inferring contagion patterns in social contact networks using a maximum likelihood approach. Nat Hazards Rev 15(3)Google Scholar
  29. Gastner M, Newman M (2006) The spatial structure of networks. Eur Phys J B 49(2):247–252CrossRefGoogle Scholar
  30. Germann TC, Kadau K, Longini I, Macken CA (2006) Mitigation strategies for pandemic inuenza in the United States. Proc Natl Acad Sci 103(15):5935–5940CrossRefGoogle Scholar
  31. Gilbert MT (2007) The emergence of hiv/aids in the americas and beyond. Proc Natl Acad Sci USA 104:18,566–18,570CrossRefGoogle Scholar
  32. González M, Lind P, Herrmann H (2006) System of mobile agents to model social networks. Phys Rev Lett 96(8):088,702CrossRefGoogle Scholar
  33. González MC, Hidalgo CA, Barabási AL (2008) Understanding individual human mobility patterns. Nature 453:779–782CrossRefGoogle Scholar
  34. Hasan S, Ukkusuri S (2011) A contagion model for understanding the propagation of hurricane warning information. Transp Res Part B 45(10):1590–1605CrossRefGoogle Scholar
  35. Haydon DT, Chase-Topping M, Shaw DJ, Matthews L, Friar JK, Wilesmith J, Woolhouse MEJ (2003) The construction and analysis of epidemic trees with reference to the 2001 UK foot-and-mouth outbreak. Proc R Soc B 270:121–127CrossRefGoogle Scholar
  36. Hoogendoorn S, Bovy P (2005) Pedestrian travel behavior modeling. Netw Spat Econ 5(2):193–216CrossRefGoogle Scholar
  37. Huerta R, Tsimring LS (2002) Contact tracing and epidemics control in social networks. Phys Rev E Stat Nonlin Soft Matter Phys 66(056):115Google Scholar
  38. Hufnagel L, Brockmann D, Geisel T (2004) Forecast and control of epidemics in a globalized world. Proc Natl Acad Sci USA 101(42):15,124–15,129CrossRefGoogle Scholar
  39. Illenberger J, Nagel K, Flötteröd G (2012) The role of spatial interaction in social networks. Netw Spat Econ 13(3):1–28Google Scholar
  40. Kempe D, Kleinberg J, Tardos É (2003) Maximizing the spread of influence though a social network. In: Proceedings of the 9th ACM SIGKDD international conference on knowledge discovery and data mining, pp 137–146Google Scholar
  41. Khani A, Hickman M, Noh H (2015) Trip-based path algorithms using the transit network hierarchy. Netw Spat Econ 15(3):635–653CrossRefGoogle Scholar
  42. Kitsak M, Gallos LK, Havlin S, Liljeros F, Muchnik L, Stanley HE, Makse HA (2010) Identification of influential spreaders in complex networks. Nat Phys 6:888–893CrossRefGoogle Scholar
  43. Kuiken C, Thakallapalli R, Eskild A, De Ronde A (2000) Genetic analysis reveals epidemiologic patterns in the spread of human immunodeficiency virus. Am J Epidemiol 152:814–822CrossRefGoogle Scholar
  44. Lam WK, Huang H (2003) Combined activity/travel choice models: time-dependent and dynamic versions. Netw Spat Econ 3(3):323–347CrossRefGoogle Scholar
  45. Meyers L, Pourbohloul B, Newman MEJ, Skowronski D, Brunham R (2005) Network theory and sars: predicting outbreak diversity. J Theor Biol 232:71–81CrossRefGoogle Scholar
  46. Murray J (2002) Mathematical biology, 3rd edn. Springer, New YorkGoogle Scholar
  47. Nassir N, Khani A, Hickman M, Noh H (2012) An intermodal optimal multi-destination tour algorithm with dynamic travel times. Transp Res Rec: J Transp Res Board 2283:57–66CrossRefGoogle Scholar
  48. Pendyala R, Kondhuri K, Chiu YC, Hickman M, Noh H, Waddell P, Wang L, You D, Gardner B (2012) Integrated land use-transport model system with dynamic time-dependent activity-travel microsimulation. Transp Res Rec: J Transp Res Board 2203:19–27CrossRefGoogle Scholar
  49. Ramadurai G, Ukkusuri S (2010) Dynamic user equilibrium model for combined activity-travel choices using activity-travel supernetwork representation. Netw Spat Econ 10(2):273–292CrossRefGoogle Scholar
  50. Rey D, Gardner L, Waller S (2016) Finding outbreak trees in networks with limited information. Netw Spat Econ 16(2):687–721CrossRefGoogle Scholar
  51. Roche B, Drake J, Rohani P (2011) An agent-based model to study the epidemiological and evolutionary dynamics of influenza viruses. BMC Bioinforma 12 (1):87CrossRefGoogle Scholar
  52. Roorda M, Carrasco J, Miller E (2009) An integrated model of vehicle transactions, activity scheduling and mode choice. Transp Res Part B 43(2):217–229CrossRefGoogle Scholar
  53. Rvachev L, Longini I (1985) A mathematical model for the global spread of influenza. Math Biosci 75:3–22CrossRefGoogle Scholar
  54. Salathé M (2010) A high-resolution human contact network for infectious disease transmission. Proc Natl Acad Sci USA 107:22,020–22,025CrossRefGoogle Scholar
  55. Schintler L, Kulkarni R, Gorman S, Stough R (2007) Using raster-based gis and graph theory to analyze complex networks. Netw Spat Econ 7(4):301–313CrossRefGoogle Scholar
  56. Small M, Tse C (2005) Small world and scale free model of transmission of sars. Int J Bifurcations Chaos Appl Sci Eng 15(1745)Google Scholar
  57. Song C, Qu Z, Blumm N, Barabási AL (2010) Limits of predictability in human mobility. Science 327:1018–1021CrossRefGoogle Scholar
  58. Stehlé J (2011) Simulation of an seir infectious disease model on the dynamic contact network of conference attendees. BMC Med 9:87CrossRefGoogle Scholar
  59. Sun L, Axhausen KW, Lee DH, Huang X (2013) Understanding metropolitan patterns of daily encounters. Proc Natl Acad Sci USA 110:13,774–13,779CrossRefGoogle Scholar
  60. Troko J, Myles P, Gibson J, Hashim A, Enstone J, Kingdon S, Packham C, Amin S, Hayward A, Van-Tam JN (2011) Is public transport a risk factor for acute respiratory infection? BMC Infect Dis 11(1):16CrossRefGoogle Scholar
  61. Wang P, Gonzlez MC, Hidalgo CA, Barabsi AL (2009) Understanding the spreading patterns of mobile phone viruses. Science 324:1071–1076CrossRefGoogle Scholar
  62. Wesolowski A, Buckee C, Bengtsson L, Wetter E, Lu X, Tatem A (2014) Commentary: containing the ebola outbreak–the potential and challenge of mobile network data. PLOS currents outbreaksGoogle Scholar
  63. Wu J, Xu F, Zhou W, Feikin D, Lin C, He X, Zhu Z, Liang W, Chin D, Schuchat A (2004) Risk factors for sars among persons without known contact with sars patients, Beijing, China. Emerg Infect Dis J-CDC 10(2):210–216CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Research Centre for Integrated Transport Innovation, School of Civil and Environmental EngineeringUniversity of New South Wales (UNSW) AustraliaSydneyAustralia
  2. 2.Department of Civil, Environmental and Geo- EngineeringUniversity of Minnesota Twin CitiesMinneapolisUSA

Personalised recommendations