Towards Identifying and Predicting Spatial Epidemics on Complex Meta-population Networks

  • Xiang LiEmail author
  • Jian-Bo Wang
  • Cong Li
Part of the Theoretical Biology book series (THBIO)


In the past decade, the network science community has witnessed huge advances in the threshold theory, prediction and control of epidemic dynamics on complex networks. While along with the understanding of spatial epidemics on meta-population networks achieved so far, more challenges have opened the door to identify, retrospect, and predict the epidemic invasion process. This chapter reviews the recent progress towards identifying susceptible-infected compartment parameters and spatial invasion pathways on a meta-population network as well as the minimal case of two-subpopulation version, which may also extend to the prediction of spatial epidemics as well. The artificial and empirical meta-population networks verify the effectiveness of our proposed solutions to the concerned problems. Finally, the whole chapter concludes with the outlook of future research.


  1. 1.
    Wiener, N.: Cybernetics: or Control and Communication in the Animal and the Machine. MIT Press, Cambridge, MA (1961)CrossRefzbMATHGoogle Scholar
  2. 2.
    Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. Macmillan, London (1976)CrossRefzbMATHGoogle Scholar
  3. 3.
    West, D.B.: Introduction to Graph Theory. Prentice Hall, Upper Saddle River (2001)Google Scholar
  4. 4.
    Erdős, P., Rényi, A.: On the evolution of random graphs. Publ. Math. Inst. Hungar. Acad. Sci. 5, 17–61 (1960)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)CrossRefzbMATHGoogle Scholar
  6. 6.
    Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Wang, X., Li, X., Chen, G.: Complex Networks: Theories and Applications. Tsinghua University Press, Beijing (2006, in Chinese)Google Scholar
  9. 9.
    Newman, M.E.J.: Networks: An Introduction. Oxford University Press, New York (2010)CrossRefzbMATHGoogle Scholar
  10. 10.
    Chen, G., Wang, X., Li, X.: Introduction to Complex Networks: Models, Structures and Dynamics. Higher Education Press, Beijing (2012)Google Scholar
  11. 11.
    Keeling, M.J., Rohani, P.: Modeling Infectious Diseases in Humans and Animals. Princeton University Press, Princeton/Oxford (2008)zbMATHGoogle Scholar
  12. 12.
    Anderson, R.M., May, R.M.: Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, Oxford (1991)Google Scholar
  13. 13.
    Heesterbeek, H., Anderson, R.M., Andreasen, V., et al.: Modeling infectious disease dynamics in the complex landscape of global health. Science 347, aaa4339 (2015)Google Scholar
  14. 14.
    Fitch, J.P.: Engineering a global response to infectious diseases. Proc. IEEE 103, 263–272 (2015)CrossRefGoogle Scholar
  15. 15.
    Brockmann, D., Helbing, D.: The hidden geometry of complex, network-driven contagion phenomena. Science 342, 1337–1342 (2013)CrossRefGoogle Scholar
  16. 16.
    McMichael, A. J.: Globalization, climate change, and human health. N. Engl. J. Med. 368, 1335–1343 (2013)CrossRefGoogle Scholar
  17. 17.
    Pastor-Satorras, R., Castellano, C., Van Mieghem, P., Vespignani, A.: Epidemic processes in complex networks. Rev. Mod. Phys. 87, 925–979 (2015)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Fu, X., Small, M., Chen, G.: Propagation Dynamics on Complex Networks: Models, Methods and Stability Analysis. Higher Education Press, Beijing (2014)CrossRefzbMATHGoogle Scholar
  19. 19.
    Li, X., Li, X.: A Data-driven inference algorithm for epidemic pathways using surveillance reports in 2009 outbreak of influenza A (H1N1). In: Proceedings of 51st IEEE Conference on Decision and Control (CDC), pp. 2840–2845 (2012)Google Scholar
  20. 20.
    Hufnagel, L., Brockmann, D., Geisel, T.: Forecast and control of epidemics in a globalized world. Proc. Natl. Acad. Sci. U. S. A. 101, 15124–15129 (2004)CrossRefGoogle Scholar
  21. 21.
    Miao, H., Xia, X., Perelson, A.S., et al.: On identifiability of nonlinear ODE models and applications in viral dynamics. SIAM Rev. 53, 3–39 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Gomez-Rodriguez, M., Leskovec, J., Krause, A.: Inferring networks of diffusion and influence. In: Proceedings of 16th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD), pp. 1019–1028 (2010)Google Scholar
  23. 23.
    Han, X., Shen, Z., Wang, W.-X., Di, Z.: Robust reconstruction of complex networks from sparse data. Phys. Rev. Lett. 114, 028701 (2015)CrossRefGoogle Scholar
  24. 24.
    Shah, D., Zaman, T.: Rumors in a network: who’s the culprit? IEEE Trans. Inf. Theory 57, 5163–5181 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Wang, Z., Dong, W., Zhang, W., Tan, C.-W.: Rumor source detection with multiple observations: fundamental limits and algorithms. In: Proceedings of the ACM Sigmetrics 2014, pp. 1–13 (2014)Google Scholar
  26. 26.
    Maeno, Y.: Discovering network behind infectious disease outbreak. Phys. A 389, 4755–4768 (2010)CrossRefGoogle Scholar
  27. 27.
    Eggo, R.-M., Cauchemez, S., Ferguson, N.M.: Spatial dynamics of the 1918 influenza pandemic in England, Wales and the United States. J. R. Soc. Interface 8, 233–243 (2011)CrossRefGoogle Scholar
  28. 28.
    Wan, X., Liu, J., Cheung, W.K., Tong, T.: Inferring epidemic network topology from surveillance data. PLoS One 9, e100661 (2014)CrossRefGoogle Scholar
  29. 29.
    Shi, B., Liu, J., Zhou, X.-N., Yang, G.-J.: Inferring plasmodium vivax transmission networks from tempo-spatial surveillance data. PLoS Negl. Trop. Dis. 8, e2682 (2014)CrossRefGoogle Scholar
  30. 30.
    Yang, X., Liu, J., Zhou, X.-N., Cheung, W.-K.: Inferring disease transmission networks at a metapopulation level. Health Inf. Sci. Syst. 17, 8 (2014)CrossRefGoogle Scholar
  31. 31.
    Gautreau, A., Barrat, A., Barthelemy, M.: Global disease spread: statistics and estimation of arrival times. J. Theor. Biol. 251, 509–522 (2008)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Balcan, D., Colizza, V., Gonçalves, B., Hu, H., Ramasco, J.J., Vespignani, A.: Multiscale mobility networks and the spatial spreading of infectious diseases. Proc. Natl. Acad. Sci. U. S. A. 106, 21484–21489 (2009)CrossRefGoogle Scholar
  33. 33.
    Wang, J.-B., Cao, L., Li X.: On estimating spatial epidemic parameters of a simplified metapopulation model. In: Proceedings of 13th IFAC Symposium on Large Scale Complex Systems: Theory and Applications, pp. 383–388 (2013)Google Scholar
  34. 34.
    Wang, J.-B., Li, X., Wang, L.: Inferring spatial transmission of epidemics in networked metapopulations. In: Proceedings of 2015 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 906–909 (2015)Google Scholar
  35. 35.
    Wang, J.-B., Wang, L., Li, X.: Identifying spatial invasion of pandemics on metapopulation networks via anatomizing arrival history. IEEE Trans. Cybern. 46, 2782–2795 (2016)CrossRefGoogle Scholar
  36. 36.
    Wang, J.-B., Li, C., Li, X.: Predicting spatial transmission at the early stage of epidemics on a networked metapopulation. In: Proceedings of 12th IEEE International Conference on Control & Automation (ICCA), pp. 116–121 (2016)Google Scholar
  37. 37.
    Li, X., Wang, J.-B., Li, C.: Towards identifying epidemic processes with interplay between complex networks and human populations. In: Proceedings of 2016 IEEE Conference on Norbert Wiener in the 21st Century (21CW), pp. 67–71 (2016)Google Scholar
  38. 38.
    Levins, R.: Some demographic and genetic consequences of environmental heterogeneity for biological control. Bull. Entomol. Soc. Am. 15, 237–240 (1969)Google Scholar
  39. 39.
    Rvachev, L.A., Longini, I.M.: A mathematical model for the global spread of influenza. Math. Biosci. 75, 3–22 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Wang, L., Li, X.: Spatial epidemiology of networked metapopulation: an overview. Chin. Sci. Bull. 59, 3511–3522 (2014)CrossRefGoogle Scholar
  41. 41.
    Brooks-Pollock, E., Roberts, G.O., Keeling, M.J.: A dynamic model of bovine tuberculosis spread and control in Great Britain. Nature 511, 228–231 (2014)CrossRefGoogle Scholar
  42. 42.
    Brockmann, D., Theis, F.: Money circulation, trackable items, and the emergence of universal human mobility patterns. IEEE Pervasive Comput. 7, 28–35 (2008)CrossRefGoogle Scholar
  43. 43.
    Wang, L., Li, X., Zhang, Y.-Q., Zhang, Y., Zhang, K.: Evolution of scaling emergence in large-scale spatial epidemic spreading. PLoS One 6, e21197 (2011)CrossRefGoogle Scholar
  44. 44.
    Barrat, A., Barthélemy, M., Pastor-Satorras, R., Vespignani, A.: The architecture of complex weighted networks. Proc. Natl. Acad. Sci. U. S. A. 101, 3747–3752 (2004)CrossRefGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Adaptive Networks and Control Lab, Department of Electronic Engineering and Research Center of Smart Networks & Systems, School of Information Science & EngineeringFudan UniversityShanghaiPeople’s Republic of China

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