Fixed-time descriptive statistics underestimate extremes of epidemic curve ensembles

07/09/2020 ∙ by Jonas L. Juul, et al. ∙ DTU 0

Across the world, scholars are racing to predict the spread of the novel coronavirus, COVID-19. Such predictions are often pursued by numerically simulating epidemics with a large number of plausible combinations of relevant parameters. It is essential that any forecast of the epidemic trajectory derived from the resulting ensemble of simulated curves is presented with confidence intervals that communicate the uncertainty associated with the forecast. Here we argue that the state-of-the-art approach for summarizing ensemble statistics does not capture crucial epidemiological information. In particular, the current approach systematically suppresses information about the projected trajectory peaks. The fundamental problem is that each time step is treated separately in the statistical analysis. We suggest using curve-based descriptive statistics to summarize trajectory ensembles. The results presented allow researchers to report more representative confidence intervals, resulting in more realistic projections of epidemic trajectories and – in turn – enable better decision making in the face of the current and future pandemics.



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The authors are thankful to the members of the SSI COVID-19 modeling group for an excellent collaboration and to Carl T. Bergstrom for comments on an early version of the manuscript. J.L.J and S.L. received additional funding through the HOPE project (Carlsberg Foundation).

Author contributions

J.L.J. and S.L. conceived the idea. J.L.J. performed simulations, analysis and calculations. K.G. and L.E.C. devised and performed epidemiological simulations. All authors contributed to discussions and wrote the manuscript.


  • Holmdahl and Buckee (2020) I. Holmdahl and C. Buckee, New England Journal of Medicine  (2020).
  • Diekmann and Heesterbeek (2000) O. Diekmann and J. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, Wiley Series in Mathematical & Computational Biology (Wiley, 2000).
  • Ferguson et al. (2005) N. M. Ferguson, D. A. Cummings, S. Cauchemez, C. Fraser, S. Riley, A. Meeyai, S. Iamsirithaworn,  and D. S. Burke, Nature 437, 209 (2005).
  • Chinazzi et al. (2020) M. Chinazzi, J. T. Davis, M. Ajelli, C. Gioannini, M. Litvinova, S. Merler, A. P. y Piontti, K. Mu, L. Rossi, K. Sun, et al., Science 368, 395 (2020).
  • Yang et al. (2020a) W. Yang, S. Kandula,  and J. Shaman,  (2020a).
  • Los Alamos National Laboratory COVID-19 team (2020) Los Alamos National Laboratory COVID-19 team, “COVID-19 Confirmed and Forecasted Case Data,”  (2020), (accessed Jun 28, 2020).
  • Johns Hopkins University Infectious Disease Dynamics COVID-19 Working Group (2020) Johns Hopkins University Infectious Disease Dynamics COVID-19 Working Group, “Covid scenario pipeline,”  (2020), (accessed Jun 28, 2020).
  • Scott (2015) D. W. Scott, Multivariate density estimation: theory, practice, and visualization (John Wiley & Sons, 2015).
  • Statens Serum Institut (2020) Statens Serum Institut, “Tillægsrapport af den 20. maj 2020.”  (2020).
  • Mirzargar et al. (2014) M. Mirzargar, R. T. Whitaker,  and R. M. Kirby, IEEE Transactions on Visualization and Computer Graphics 20, 2654 (2014).
  • Sun and Genton (2011) Y. Sun and M. G. Genton, Journal of Computational and Graphical Statistics 20, 316 (2011).
  • Srinivasan et al. (2020) S. Srinivasan, K. B. Ramadi, F. Vicario, D. Gwynne, A. Hayward, D. Lagier, R. Langer, J. J. Frassica, R. M. Baron,  and G. Traverso, Science Translational Medicine  (2020).
  • Yang et al. (2020b) X. Yang, Y. Yu, J. Xu, H. Shu, H. Liu, Y. Wu, L. Zhang, Z. Yu, M. Fang, T. Yu, et al., The Lancet Respiratory Medicine  (2020b).