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Exploring Concurrency and Reachability in the Presence of High Temporal Resolution

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Part of the Computational Social Sciences book series (CSS)

Abstract

Network properties govern the rate and extent of spreading processes on networks, from simple contagions to complex cascades. Recent advances have extended the study of spreading processes from static networks to temporal networks, where nodes and links appear and disappear. We review previous studies on the effects of temporal connectivity for understanding the spreading rate and outbreak size of model infection processes. We focus on the effects of “accessibility”, whether there is a temporally consistent path from one node to another, and “reachability”, the density of the corresponding “accessibility graph” representation of the temporal network. We study reachability in terms of the overall level of temporal concurrency between edges, quantifying the overlap of edges in time. We explore the role of temporal resolution of contacts by calculating reachability with the full temporal information as well as with a simplified interval representation approximation that demands less computation. We demonstrate the extent to which the computed reachability changes due to this simplified interval representation.

Keywords

Temporal networks Concurrency Accessibility Reachability Temporal contacts Structural cohesion Disease spread Epidemic potential STD 

Notes

Acknowledgements

We thank Petter Holme and Jari Saramäki for the invitation to write this chapter. Research reported in this publication was supported by the Eunice Kennedy Shriver National Institute of Child Health and Human Development of the National Institutes of Health under Award Number R01HD075712. Additional support was provided by the James S. McDonnell Foundation 21st Century Science Initiative—Complex Systems Scholar Award (grant #220020315) and by the Army Research Office (MURI award W911NF-18-1-0244). The content is solely the responsibility of the authors and does not necessarily represent the official views of any supporting agency.

References

  1. 1.
    Armbruster, B., Wang, L., Morris, M.: Forward reachable sets: analytically derived properties of connected components for dynamic networks. Netw. Sci. 5(3), 328–354 (2017)CrossRefGoogle Scholar
  2. 2.
    Daley, D.J., Kendall, D.G.: Epidemics and rumours. Nature 204(4963), 1118 (1964)ADSCrossRefGoogle Scholar
  3. 3.
    Doherty, I.A., Shiboski, S., Ellen, J.M., Adimora, A.A., Padian, N.S.: Sexual bridging socially and over time: a simulation model exploring the relative effects of mixing and concurrency on viral sexually transmitted infection transmission. Sex. Transm. Dis. 33(6), 368–373 (2006)CrossRefGoogle Scholar
  4. 4.
    Eames, K.T.D., Keeling, M.J.: Monogamous networks and the spread of sexually transmitted diseases. Math. Biosci. 189(2), 115–130 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Epstein, H., Morris, M.: Concurrent partnerships and HIV: an inconvenient truth. J. Int. AIDS Soc. 14(1), 13 (2011)CrossRefGoogle Scholar
  6. 6.
    Fournet, J., Barrat, A.: Contact patterns among high school students. PLoS One 9(9), 1–17 (2014)CrossRefGoogle Scholar
  7. 7.
    Gernat, T., Rao, V.D., Middendorf, M., Dankowicz, H., Goldenfeld, N., Robinson, G.E.: Automated monitoring of behavior reveals bursty interaction patterns and rapid spreading dynamics in honeybee social networks. Proc. Natl. Acad. Sci. U.S.A. 115(7), 1433–1438 (2018)ADSCrossRefGoogle Scholar
  8. 8.
    Gurski, K., Hoffman, K.: Influence of concurrency, partner choice, and viral suppression on racial disparity in the prevalence of HIV infected women. Math. Biosci. 282, 91–108 (2016)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Holme, P.: Network reachability of real-world contact sequences. Phys. Rev. E 71, 046119 (2005)ADSCrossRefGoogle Scholar
  10. 10.
    Holme, P., Liljeros, F.: Birth and death of links control disease spreading in empirical contact networks. Sci. Rep. 4(1), 4999 (2015)CrossRefGoogle Scholar
  11. 11.
    Holme, P., Saramäki, J.: Temporal networks. Phys. Rep. 519(3), 97–125 (2012)ADSCrossRefGoogle Scholar
  12. 12.
    Isella, L., Stehlé, J., Barrat, A., Cattuto, C., Pinton, J.F., den Broeck, W.V.: What’s in a crowd? Analysis of face-to-face behavioral networks. J. Theor. Biol. 271(1), 166–180 (2011)zbMATHGoogle Scholar
  13. 13.
    Karsai, M., Kivelä, M., Pan, R.K., Kaski, K., Kertész, J., Barabási, A.L., Saramäki, J.: Small but slow world: how network topology and burstiness slow down spreading. Phys. Rev. E 83, 025102 (2011)ADSCrossRefGoogle Scholar
  14. 14.
    Kretzschmar, M., Morris, M.: Measures of concurrency in networks and the spread of infectious disease. Math. Biosci. 133(2), 165–195 (1996)zbMATHCrossRefGoogle Scholar
  15. 15.
    Lee, E., Emmons, S., Gibson, R., Moody, J., Mucha, P.J.: Concurrency and reachability in tree-like temporal networks. http://arxiv.org/abs/1905.08580 (2019)
  16. 16.
    Lentz, H.H.K., Selhorst, T., Sokolov, I.M.: Unfolding accessibility provides a macroscopic approach to temporal networks. Phys. Rev. Lett. 110, 118701 (2013)ADSCrossRefGoogle Scholar
  17. 17.
    Li, M., Rao, V.D., Gernat, T., Dankowicz, H.: Lifetime-preserving reference models for characterizing spreading dynamics on temporal networks. Sci. Rep. 8(1), 709 (2018)ADSCrossRefGoogle Scholar
  18. 18.
    Lurie, M.N., Rosenthal, S.: The concurrency hypothesis in sub-saharan Africa: Convincing empirical evidence is still lacking. Response to Mah and Halperin, Epstein, and Morris. AIDS Behav. 14(1), 34–37 (2010)CrossRefGoogle Scholar
  19. 19.
    Mah, T.L., Halperin, D.T.: The evidence for the role of concurrent partnerships in africa’s HIV epidemics: a response to Lurie and Rosenthal. AIDS Behav. 14(1), 25–28 (2010)CrossRefGoogle Scholar
  20. 20.
    Masuda, N., Lambiotte, R.: A Guide to Temporal Networks. World Scientific, Singapore (2016)zbMATHCrossRefGoogle Scholar
  21. 21.
    Masuda, N., Klemm, K., Eguíluz, V.M.: Temporal networks: slowing down diffusion by long lasting interactions. Phys. Rev. Lett. 111, 188701 (2013)ADSCrossRefGoogle Scholar
  22. 22.
    May, R.M., Anderson, R.M.: Transmission dynainics of HIV infection. Nature 326, 137–142 (1987)ADSCrossRefGoogle Scholar
  23. 23.
    May, R.M., Anderson, R.M.: The transmission dynamics of human immunodeficiency virus (HIV). Trans. R. Soc. Lond. B 321, 565–607 (1988)ADSGoogle Scholar
  24. 24.
    Miller, J.C., Slim, A.C.: Saturation effects and the concurrency hypothesis: insights from an analytic model. PLoS One 12(11), e0187938 (2017)CrossRefGoogle Scholar
  25. 25.
    Moody, J.: The importance of relationship timing for diffusion: indirect connectivity and STD infections risk. Soc. Forces 81(1), 25–56 (2002)CrossRefGoogle Scholar
  26. 26.
    Moody, J., Benton, R.A.: Interdependent effects of cohesion and concurrency for epidemic potential. Ann. Epidemiol. 26(4), 241–248 (2016)CrossRefGoogle Scholar
  27. 27.
    Moody, J., White, D.R.: Structural cohesion and embeddedness: a hierarchical concept of social groups. Am. Sociol. Rev. 68(1), 103–127 (2003)CrossRefGoogle Scholar
  28. 28.
    Morris, M., Kretzschmar, M.: Concurrent partnerships and transmission dynamics in networks. Soc. Netw. 17(3), 299–318 (1995)CrossRefGoogle Scholar
  29. 29.
    Morris, M., Epstein, H., Wawer, M.: Timing is everything: international variations in historical sexual partnership concurrency and HIV prevalence. PLoS One 5(11), e14092 (2010)ADSCrossRefGoogle Scholar
  30. 30.
    Onaga, T., Gleeson, J.P., Masuda, N.: Concurrency-induced transitions in epidemic dynamics on temporal networks. Phys. Rev. Lett. 119, 108301 (2017)ADSCrossRefGoogle Scholar
  31. 31.
    Rocha, L.E.C., Liljeros, F., Holme, P.: Information dynamics shape the sexual networks of internet-mediated prostitution. Proc. Natl. Acad. Sci. 107(13), 5706–5711 (2010)ADSzbMATHCrossRefGoogle Scholar
  32. 32.
    Rocha, L.E.C., Liljeros, F., Holme, P.: Simulated epidemics in an empirical spatiotemporal network of 50,185 sexual contacts. PLoS. Comput. Biol. 7(3), 1–9 (2011)CrossRefGoogle Scholar
  33. 33.
    Vazquez, A., Rácz, B., Lukács, A., Barabási, A.L.: Impact of non-poissonian activity patterns on spreading processes. Phys. Rev. Lett. 98, 158702 (2007)ADSCrossRefGoogle Scholar
  34. 34.
    Watts, C.H., May, R.M.: The influence of concurrent partnerships on the dynamics of HIV/AIDS. Math. Biosci. 108(1), 89–104 (1992)zbMATHCrossRefGoogle Scholar
  35. 35.
    White, D., Newman, M.: Fast approximation algorithms for finding node-independent paths in networks. Santa Fe Institute Working Papers Series (2001). Available at SSRN: https://ssrn.com/abstract=1831790 or http://dx.doi.org/10.2139/ssrn.1831790

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of North CarolinaChapel HillUSA
  2. 2.Duke UniversityDurhamUSA

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