Advertisement

Bulletin of Mathematical Biology

, Volume 68, Issue 8, pp 1893–1921 | Cite as

The Modeling of Global Epidemics: Stochastic Dynamics and Predictability

  • V. ColizzaEmail author
  • A. Barrat
  • M. Barthélemy
  • A. Vespignani
Original Article

Abstract

The global spread of emergent diseases is inevitably entangled with the structure of the population flows among different geographical regions. The airline transportation network in particular shrinks the geographical space by reducing travel time between the world's most populated areas and defines the main channels along which emergent diseases will spread. In this paper, we investigate the role of the large-scale properties of the airline transportation network in determining the global propagation pattern of emerging diseases. We put forward a stochastic computational framework for the modeling of the global spreading of infectious diseases that takes advantage of the complete International Air Transport Association 2002 database complemented with census population data. The model is analyzed by using for the first time an information theory approach that allows the quantitative characterization of the heterogeneity level and the predictability of the spreading pattern in presence of stochastic fluctuations. In particular we are able to assess the reliability of numerical forecast with respect to the intrinsic stochastic nature of the disease transmission and travel flows. The epidemic pattern predictability is quantitatively determined and traced back to the occurrence of epidemic pathways defining a backbone of dominant connections for the disease spreading. The presented results provide a general computational framework for the analysis of containment policies and risk forecast of global epidemic outbreaks.

Keywords

Complex networks Epidemiology 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albert, R., Barabási, A.-L., 2000. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97.CrossRefGoogle Scholar
  2. Amaral, L.A.N., Scala, A., Barthélemy, M., Stanley, H.E., 2000. Classes of small-world networks. Proc. Natl. Acad. Sci. U.S.A. 97, 11149–11152.CrossRefGoogle Scholar
  3. Anderson, R.M., May, R.M., 1992. Infectious Diseases in Humans. Oxford University Press, Oxford, p. 4Google Scholar
  4. Baroyan, O.V., Genchikov, L.A., Rvachev, L.A., Shashkov, V.A., 1969. An attempt at large-scale influenza epidemic modelling by means of a computer. Bull. Int. Epidemiol. Assoc. 18, 22–31.Google Scholar
  5. Barrat, A., Barthélemy, M., Pastor-Satorras, R., Vespignani, A., 2004. The architecture of complex weighted networks. Proc. Natl. Acad. Sci. U.S.A. 101, 3747–3752.CrossRefGoogle Scholar
  6. Chowell, G., Hyman, J.M., Eubank, S., Castillo-Chavez, C., 2003. Scaling laws for the movement of people between locations in a large city. Phys. Rev. E 68, 066102.CrossRefGoogle Scholar
  7. Cliff, A., Haggett, P., 2004. Time, travel and infection. Br. Med. Bull. 69, 87–99.CrossRefGoogle Scholar
  8. Cohen, M.L., 2000. Changing patterns of infectious disease. Nature 406, 762–767.CrossRefGoogle Scholar
  9. Dickman, R., 1994. Numerical study of a field theory for directed percolation. Phys. Rev. E 50, 4404–4409.CrossRefGoogle Scholar
  10. Dorogovtsev, S.N., Mendes, J.F.F., 2003. Evolution of Networks: From Biological Nets to the Internet and WWW. Oxford University Press, Oxford.zbMATHGoogle Scholar
  11. Eubank, S., Guclu, H., Anil Kumar, V.S., Marathe, M.V., Srinivasan, A., Toroczkai, Z., Wang, N., 2004. Modelling disease outbreaks in realistic urban social networks. Nature 429, 180–184.CrossRefGoogle Scholar
  12. Ferguson, N.M., Keeling, M.J., Edmunds, W.J., Gani, R., Grenfell, B.T., Anderson, R.M., Leach, S., 2003. Planning for smallpox outbreaks. Nature 425, 681–685.CrossRefGoogle Scholar
  13. Flahault, A., Valleron, A.-J., 1991. A method for assessing the global spread of HIV-1 infection based on air-travel. Math. Pop. Studies 3, 1–11.Google Scholar
  14. Gardiner W.C., 2004. Handbook of Stochastic Methods for Physics, Chemistry and Natural Sciences, 3rd ed. Springer, New York.Google Scholar
  15. Gastner, M.T., Newman, M.E.J., 2004. Diffusion-based method for producing density-equalizing maps. Proc. Natl. Acad. Sci. U.S.A. 101, 7499–7504.zbMATHCrossRefMathSciNetGoogle Scholar
  16. Gillespie, D.T., 2000. The chemical Langevin equation. J. Chem. Phys. 113, 297–306.CrossRefGoogle Scholar
  17. Grais, R.F., Hugh Ellis, J., Glass, G.E., 2003. Assessing the impact of airline travel on the geographic spread of pandemic influenza. Eur. J. Epidemiol. 18, 1065–1072.CrossRefGoogle Scholar
  18. Grais, R.F., Hugh Ellis, J., Kress, A., Glass, G.E., 2004. Modeling the spread of annual influenza epidemics in the U.S.: The potential role of air travel. Health Care Manage. Sci. 7, 127–134.CrossRefGoogle Scholar
  19. Guimerà, R., Mossa, S., Turtschi, A., Amaral, L.A.N., 2005. The worldwide air transportation network: Anomalous centrality, community structure, and cities’ global roles. Proc. Natl. Acad. Sci. U.S.A. 102, 7794–7799.CrossRefGoogle Scholar
  20. Hethcote, H.W., Yorke, J.A., 1984. Gonnorhea: Transmission Dynamics and Control. Lecture Notes in Biomathematics 56. Springer-Verlag, Berlin.Google Scholar
  21. Hufnagel, L., Brockmann, D., Geisel, T., 2004. Forecast and control of epidemics in a globalized world. Proc. Natl. Acad. Sci. U.S.A. 101, 15124–15129.CrossRefGoogle Scholar
  22. Institute of Medicine 1992. Emerging Infections: Microbial Threats to Health in the United States. National Academy Press, Washington, DC.Google Scholar
  23. Keeling, M.J., 1999. The effects of local spatial structure on epidemiological invasions. Proc. R. Soc. Lond. B 266, 859–867.CrossRefGoogle Scholar
  24. Keeling, M.J., et al., 2001. Dynamics of the 2001 UK foot and mouth epidemic: Stochastic dispersal in a heterogeneous landscape. Science 294, 813–817.CrossRefGoogle Scholar
  25. Kretzschmar, M., Morris, M., 1996. Measures of concurrency in networks and the spread of infectious disease. Math. Biosci. 133, 165–195.zbMATHCrossRefGoogle Scholar
  26. Lipsitch, M. et al., 2003. Transmission dynamics and control of Severe Acute Respiratory Syndrome. Science 300, 1966.CrossRefGoogle Scholar
  27. Lee, L., 1999. Paper presented in the 37th Annual Meeting of the Association for Computational Linguistics, pp. 25–32.Google Scholar
  28. Lloyd, A.L., May, R.M., 2001. How viruses spread among computers and people. Science 292, 1316–1317.CrossRefGoogle Scholar
  29. Longini, I.M., 1988. A mathematical model for predicting the geographic spread of new infectious agents. Math. Biosci. 90, 367–383.CrossRefMathSciNetGoogle Scholar
  30. Marro, J., Dickman, R., 1998. Nonequilibrium Phase Transitions and Critical Phenomena. Cambridge University Press, Cambridge, UK.Google Scholar
  31. Meyers, L.A., Pourbohloul, B., Newman, M.E.J., Skowronski, D.M., and Brunham, R.C., 2005. Network theory and SARS: Predicting outbreak diversity. J. Theor. Biol. 232, 71–81.CrossRefMathSciNetGoogle Scholar
  32. Murray, J.D., 1993. Mathematical Biology, 2nd ed. Springer, New York.zbMATHGoogle Scholar
  33. Pastor-Satorras, R., Vespignani, A., 2001. Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 3200–3203.CrossRefGoogle Scholar
  34. Pastor-Satorras, R., Vespignani, A., 2003. Evolution and Structure of the Internet: A Statistical Physics Approach. Cambridge University Press, Cambridge, UK.Google Scholar
  35. Riley, S., et al., 2003. Transmission dynamics of the etiological agent of SARS in Hong Kong: Impact of public health interventions. Science 300, 1961–1966.CrossRefGoogle Scholar
  36. Rvachev, L.A., Longini, I.M., 1985. A mathematical model for the global spread of influenza. Math. Biosci. 75, 3–22.zbMATHCrossRefMathSciNetGoogle Scholar
  37. Wong, S.K.M., Yao Y.Y., 1987. SIGIR '87: Proceedings of the 10th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval. ACM Press, New York, pp. 3–12.CrossRefGoogle Scholar
  38. Zipf, G.K., 1949. Human Behavior and the Principle of Least Efforts. Addison-Wesley, Reading, MA.Google Scholar

Copyright information

© Society for Mathematical Biology 2006

Authors and Affiliations

  • V. Colizza
    • 1
    Email author
  • A. Barrat
    • 2
  • M. Barthélemy
    • 1
  • A. Vespignani
    • 1
  1. 1.School of Informatics and Center for BiocomplexityIndiana UniversityBloomingtonUSA
  2. 2.Unité Mixte de Recherche du CNRS 8627, LPT, Bâtiment 210Université de Paris-SudORSAY CedexFrance

Personalised recommendations