Integrating Epidemiological Modeling and Surveillance Data Feeds: A Kalman Filter Based Approach

  • Weicheng Qian
  • Nathaniel D. Osgood
  • Kevin G. Stanley
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8393)


Infectious disease spread is difficult to accurately measure and model. Even for well-studied pathogens, uncertainties remain regarding dynamics of mixing behavior and how to balance simulation-generated estimates with empirical data. While Markov Chain Monte Carlo approaches sample posteriors given empirical data, health applications of such methods have not considered dynamics associated with model error. We present here an Extended Kalman Filter (EKF) approach for recurrent simulation regrounding as empirical data arrives throughout outbreaks. The approach simultaneously considers empirical data accuracy, growing simulation error between measurements, and supports estimation of changing model parameters. We evaluate our approach using a two-level system, with “ground truth” generated by an agent-based model simulating epidemics over empirical microcontact networks, and noisy measurements fed into an EKF corrected aggregate model. We find that the EKF solution improves outbreak peak estimation and can compensate for inaccuracies in model structure and parameter estimates.


Kalman Filter simulation epidemiology 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Tuite, A., Greer, A., Whelan, M., Winter, A., Lee, B., Yan, P., Wu, J., Moghadas, S., Buckeridge, D., Pourbohloul, B., et al.: Estimated epidemiologic parameters and morbidity associated with pandemic H1N1 influenza. Canadian Medical Association Journal 182(2), 131–136 (2010)CrossRefGoogle Scholar
  2. 2.
    Keeling, M.: The implications of network structure for epidemic dynamics. Theoretical Population Biology 67(1), 1–8 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Hashemian, M., Qian, W., Stanley, K.G., Osgood, N.D.: Temporal aggregation impacts on epidemio- logical simulations employing microcontact data. BMC Medical Informatics and Decision Making 12(1), 132 (2012)CrossRefGoogle Scholar
  4. 4.
    Machens, A., Gesualdo, F., Rizzo, C., Tozzi, A.E., Barrat, A., Cattuto, C.: An infectious disease model on empirical networks of human contact: bridging the gap between dynamic network data and contact matrices. BMC Infectious Diseases 13(1), 185 (2013)CrossRefGoogle Scholar
  5. 5.
    Mbalawata, I.S., Särkkä, S., Haario, H.: Parameter estimation in stochastic differential equations with markov chain monte carlo and non-linear kalman filtering. Computational Statistics, 1–29 (2012)Google Scholar
  6. 6.
    Dorigatti, I., Cauchemez, S., Pugliese, A., Ferguson, N.M.: A new approach to characterising infectious disease transmission dynamics from sentinel surveillance: Application to the italian 2009–2010 a H1N1 influenza pandemic. Epidemics 4(1), 9–21 (2012)CrossRefGoogle Scholar
  7. 7.
    Coelho, F.C., Codeço, C.T., Gomes, M.G.M.: A bayesian framework for parameter estimation in dynam- ical models. PloS One 6(5), e19616 (2011)Google Scholar
  8. 8.
    Osgood, N., Liu, J.: Bayesian parameter estimation of system dynamics models using markov chain monte carlo methods: An informal introduction. In: The 30th International Conference of the System Dynamics Society, p. 19. Curran Associates, Inc, New York (2013)Google Scholar
  9. 9.
    Tian, Y., Osgood, N.: Comparison between individual-based and aggregate models in the context of tuberculosis transmission. In: The 29th International Conference of the System Dynamics Society, Washington, D.C, p. 29 (2011)Google Scholar
  10. 10.
    Wang, F.Y.: Toward a revolution in transportation operations: Ai for complex systems. IEEE Intelligent Systems 23(6), 8–13 (2008)CrossRefzbMATHGoogle Scholar
  11. 11.
    Rahmandad, H., Sterman, J.: Heterogeneity and network structure in the dynamics of diffusion: Comparing agent-based and differential equation models. Management Science 54(5), 998–1014 (2008)CrossRefGoogle Scholar
  12. 12.
    Obeidat, M.: Bayesian estimation of time series of counts. Presentation at the 41st Annual Meeting of the Statistical Society of Canada, Edmonton, May 26-29 (2013)Google Scholar
  13. 13.
    Chiogna, M., Gaetan, C.: Hierarchical space-time modelling of epidemic dynamics: an application to measles outbreaks. Statistical Methods and Applications 13(1), 55–71 (2004)zbMATHMathSciNetGoogle Scholar
  14. 14.
    Cazelles, B., Chau, N.: Using the kalman filter and dynamic models to assess the changing hiv/aids epidemic. Mathematical Biosciences 140(2), 131–154 (1997)CrossRefzbMATHGoogle Scholar
  15. 15.
    Chiogna, M., Gaetan, C.: Dynamic generalized linear models with application to environmental epidemiology. Journal of the Royal Statistical Society: Series C (Applied Statistics) 51(4), 453–468 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Eagle, N., Pentland, A.S., Lazer, D.: Inferring friendship network structure by using mobile phone data. Proceedings of the National Academy of Sciences 106(36), 15274–15278 (2009)CrossRefGoogle Scholar
  17. 17.
    Salathé, M., Kazandjieva, M., Lee, J.W., Levis, P., Feldman, M.W., Jones, J.H.: A high-resolution human contact network for infectious disease transmission. Proceedings of the National Academy of Sciences 107(51), 22020–22025 (2010)CrossRefGoogle Scholar
  18. 18.
    Hashemian, M., Stanley, K., Osgood, N.: Leveraging H1N1 infection transmission modeling with proximity sensor microdata. BMC Medical Informatics and Decision Making 12(1), 35 (2012)CrossRefGoogle Scholar
  19. 19.
    Funk, S., Salathé, M., Jansen, V.A.: Modelling the influence of human behaviour on the spread of infectious diseases: a review. Journal of The Royal Society Interface 7(50), 1247–1256 (2010)CrossRefGoogle Scholar
  20. 20.
    Gelb, A.: Applied optimal estimation. MIT Press (1974)Google Scholar
  21. 21.
    Osgood, N.: Using traditional and agent based toolset for system dynamics: Present tradeoffs and future evolution. System Dynamics (2007)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Weicheng Qian
    • 1
  • Nathaniel D. Osgood
    • 1
  • Kevin G. Stanley
    • 1
  1. 1.Department of Computer ScienceUniversity of SaskatchewanCanada

Personalised recommendations