Uncertainty in On-The-Fly Epidemic Fitting

  • Roxana Danila
  • Marily Nika
  • Thomas Wilding
  • William J. Knottenbelt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8721)


The modern world features a plethora of social, technological and biological epidemic phenomena. These epidemics now spread at unprecedented rates thanks to advances in industrialisation, transport and telecommunications. Effective real-time decision making and management of modern epidemic outbreaks depends on the two factors: the ability to determine epidemic parameters as the epidemic unfolds, and the ability to characterise rigorously the uncertainties inherent in these parameters. This paper presents a generic maximum-likelihoodbased methodology for online epidemic fitting of SIR models from a single trace which yields confidence intervals on parameter values. The method is fully automated and avoids the laborious manual efforts traditionally deployed in the modelling of biological epidemics. We present case studies based on both synthetic and real data.


Epidemics Compartmental disease models SIR models Maximum likelihood estimation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Anderson, H., Britton, T.: Stochastic Epidemic Models and their Statistical Analysis. Springer (2000)Google Scholar
  2. 2.
    Angulo, J., Yu, H., Langousis, A., Kolovos, A., Wang, J., Madrid, A., Christakos, G.: Spatiotemporal Infectious Disease Modeling: A BME-SIR Approach. PLoS ONE (2013)Google Scholar
  3. 3.
    Bakshy, E., Rosenn, I., Marlow, C., Adamic, L.: The Role of Social Networks in Information Diffusion. In: Proc. 21st International Conference on the World Wide Web, WWW 2012 (2012)Google Scholar
  4. 4.
    Bauer, F., Lizier, J.: Identifying Influential Spreaders. CoRR, abs/1203.0502 (2012)Google Scholar
  5. 5.
    Bolker, B., Ellner, S.: Likelihood and all that, for Disease Ecologists (2011),
  6. 6.
    Briggs, A., Weinstein, M., Fenwick, E., Karnon, J., Sculpher, M., Paltiel, A.: Model Parameter Estimation and Uncertainty: A Report of the ISPOR-SMDM Modeling Good Research Practices Task Force-6. Value in Health 15(6), 835–842 (2012)CrossRefGoogle Scholar
  7. 7.
    Brooks-Pollock, E., Eames, K.: Pigs didn’t Fly, but Swine Flu. Mathematics Today 47, 36–40 (2011)MathSciNetGoogle Scholar
  8. 8.
    Burr, T., Chowell, G.: Observation and Model Error Effects on Parameter Estimates in Susceptible-Infected-Recovered Epidemiological Models. Far East Journal of Theoretical Statistics 19(2), 163–183 (2013)MathSciNetGoogle Scholar
  9. 9.
    Christley, R., Mort, M., Wynne, B., Wastling, J., Heathwaite, A., Pickup, R., Austin, Z., Latham, S.: “Wrong, but Useful”: Negotiating Uncertainty in Infectious Disease Modelling. PLoS One 8(10), e76277, 10 (2013)Google Scholar
  10. 10.
    Dolgoarshinnykh, R.: Epidemic Modelling Graduate Topics Course. Lecture Notes,
  11. 11.
    Elderd, B., Vanja, M., Dukic, V., Dwyer, G.: Uncertainty in Predictions of Disease Spread and Public Health Responses to Bioterrorism and Emerging Diseases. Proceedings of the National Academy of Sciences 103(42), 15693–15697 (2006)CrossRefGoogle Scholar
  12. 12.
    Flanders, W., Kleinbaum, D.: Basic Models for Disease Occurrence in Epidemiology. International Journal of Epidemiology 24(1), 1–7 (1995)CrossRefGoogle Scholar
  13. 13.
    Gilbert, J., Meyers, L., Galvani, A., Townsend, J.: Probabilistic Uncertainty Analysis of Epidemiological Modeling to Guide Public Health Intervention Policy. Epidemics 6, 37–45 (2014)CrossRefGoogle Scholar
  14. 14.
    Hartmann, W., Manchanda, P., Nair, H., Bothner, M., Dodds, P., Godes, D., Hosanagar, K., Tucker, C.: Modeling Social Interactions: Identification, Empirical Methods and Policy Implications. Marketing Letters 19(3), 287–304 (2008)CrossRefGoogle Scholar
  15. 15.
    Hethcote, H.: The Mathematics of Infectious Diseases. SIAM Review 42(4), 599–653 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Keeling, M.: State-Of-Science Review: Predictive and Real-time Epidemiological Modellig (2006),
  17. 17.
    Kermack, W., McKendrick, A.: A Contribution to the Mathematical Theory of Epidemics. Proceedings of the Royal Society of London. Series A 115(772), 700–721 (1927)CrossRefzbMATHGoogle Scholar
  18. 18.
    Lagarias, J., Reeds, J., Wright, M., Wright, P.: Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions. SIAM Journal of Optimization 9, 112–147 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Lerner, R.: The Black Death and Western European Eschatological Mentalities. The American Historical Review 86, 533–552 (1981)CrossRefGoogle Scholar
  20. 20.
    Nika, M., Fiems, D., Turck, K., Knottenbelt, W.J.: Modelling Interacting Epidemics in Overlapping Populations. In: Proc. 21st International Conference on Analytical & Stochastic Modelling Techniques & Applications (ASMTA 2014), Budapest, Hungary (2014)Google Scholar
  21. 21.
    Nika, M., Ivanova, G., Knottenbelt, W.J.: On Celebrity, Epidemiology and the Internet. In: Proc. 7th International Conference on Performance Evaluation Methodologies and Tools (VALUETOOLS), Turin, Italy (December 2013)Google Scholar
  22. 22.
    Tizzoni, M., Bajardi, P., Poletto, C., Ramasco, J., Balcan, D., Goncalves, B., Perra, N., Colizza, V., Vespignani, A.: Real-time Numerical Forecast of Global Epidemic Spreading: Case study of 2009 A/H1N1pdm. BMC Medicine 10(1), 165 (2012)CrossRefGoogle Scholar
  23. 23.
    Tweedle, V., Smith, R.: A Mathematical Model of Bieber Fever: The most infectious disease of our time. In: Mushayabasa, S., Bhunu, C.P. (eds.) Understanding the Dynamics of Emerging and Re-Emerging Infectious Diseases using Mathematical Models, ch. 7, pp. 157–177. Transworld Research Network (2012)Google Scholar
  24. 24.
    Venzon, D., Moolgavkar, S.: A Method for Computing Profile-Likelihood-Based Confidence Intervals. Applied Statistics 37(1), 87–94 (1988)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Roxana Danila
    • 1
  • Marily Nika
    • 1
  • Thomas Wilding
    • 1
  • William J. Knottenbelt
    • 1
  1. 1.Department of ComputingImperial College LondonLondonUK

Personalised recommendations