The Annals of Applied Statistics

Forecasting seasonal influenza with a state-space SIR model

Dave Osthus, Kyle S. Hickmann, Petruţa C. Caragea, Dave Higdon, and Sara Y. Del Valle

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Abstract

Seasonal influenza is a serious public health and societal problem due to its consequences resulting from absenteeism, hospitalizations, and deaths. The overall burden of influenza is captured by the Centers for Disease Control and Prevention’s influenza-like illness network, which provides invaluable information about the current incidence. This information is used to provide decision support regarding prevention and response efforts. Despite the relatively rich surveillance data and the recurrent nature of seasonal influenza, forecasting the timing and intensity of seasonal influenza in the U.S. remains challenging because the form of the disease transmission process is uncertain, the disease dynamics are only partially observed, and the public health observations are noisy. Fitting a probabilistic state-space model motivated by a deterministic mathematical model [a susceptible-infectious-recovered (SIR) model] is a promising approach for forecasting seasonal influenza while simultaneously accounting for multiple sources of uncertainty. A significant finding of this work is the importance of thoughtfully specifying the prior, as results critically depend on its specification. Our conditionally specified prior allows us to exploit known relationships between latent SIR initial conditions and parameters and functions of surveillance data. We demonstrate advantages of our approach relative to alternatives via a forecasting comparison using several forecast accuracy metrics.

Article information

Source
Ann. Appl. Stat. Volume 11, Number 1 (2017), 202-224.

Dates
Received: September 2015
Revised: September 2016
First available in Project Euclid: 8 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1491616878

Digital Object Identifier
doi:10.1214/16-AOAS1000

Keywords
Bayesian modeling state-space modeling SIR model forecasting influenza time-series

Citation

Osthus, Dave; Hickmann, Kyle S.; Caragea, Petruţa C.; Higdon, Dave; Del Valle, Sara Y. Forecasting seasonal influenza with a state-space SIR model. Ann. Appl. Stat. 11 (2017), no. 1, 202--224. doi:10.1214/16-AOAS1000. https://projecteuclid.org/euclid.aoas/1491616878.


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References

  • Anderson, J. L. (2001). An ensemble adjustment Kalman filter for data assimilation. Mon. Weather Rev. 129 2884–2903.
  • Brauer, F., van den Driessche, P. and Wu, J., eds. (2008). Mathematical Epidemiology. Lecture Notes in Math. 1945. Springer, Berlin.
  • Capaldi, A., Behrend, S., Berman, B., Smith, J., Wright, J. and Lloyd, A. L. (2012). Parameter estimation and uncertainty quantification for an epidemic model. Math. Biosci. Eng. 9 553–576.
  • CDC.gov (2017). Influenza (Flu) Past Pandemics. Available at http://www.cdc.gov/flu/pandemic-resources/basics/past-pandemics.html. Accessed: 02-06-2017.
  • Centers for Disease Control and Prevention (2014a). Free resources. Available at http://www.cdc.gov/flu/freeresources/. Accessed: 05-5-2015.
  • Centers for Disease Control and Prevention (2014b). Estimating Seasonal Influenza-Associated Deaths in the United States. Available at http://www.cdc.gov/flu/about/disease/us_flu-related_deaths.htm. Accessed: 02-06-2017.
  • Centers for Disease Control and Prevention (2015). In Overview of influenza surveillance in the United States. Available at http://www.cdc.gov/flu/weekly/overview.htm. Accessed: 04-30-2015.
  • Chretien, J.-P., George, D., Shaman, J., Chitale, R. A. and McKenzie, F. E. (2014). Influenza forecasting in human populations: A scoping review. PLoS ONE 9 e94130.
  • Dukic, V., Lopes, H. F. and Polson, N. G. (2012). Tracking epidemics with Google Flu Trends data and a state-space SEIR model. J. Amer. Statist. Assoc. 107 1410–1426.
  • Gelman, A. and Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statist. Sci. 7 457–472.
  • Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6 721–741.
  • Generous, N., Fairchild, G., Deshpande, A., Valle, S. Y. D. and Priedhorsky, R. (2014). Global disease monitoring and forecasting with Wikipedia. PLoS Comput. Biol. 10 e1003892.
  • Germann, T. C., Kadau, K., Longini, I. M. and Macken, C. A. (2006). Mitigation strategies for pandemic influenza in the United States. Proc. Natl. Acad. Sci. USA 103 5935–5940.
  • Ginsberg, J., Mohebbi, M. H., Patel, R. S., Brammer, L., Smolinski, M. S. and Brilliant, L. (2009). Detecting influenza epidemics using search engine query data. Nature 457 1012–1014.
  • Harris, K. M., Maurer, J. and Kellermann, A. L. (2010). Influenza vaccine. N. Engl. J. Med. 363 2183–2185.
  • Heffernan, J., Smith, R. and Wahl, L. (2005). Perspectives on the basic reproductive ratio. J. Roy. Soc. Interface 2 281–293.
  • Hickmann, K. S., Fairchild, G., Priedhorsky, R., Generous, N., Hyman, J. M., Deshpande, A. and Valle, S. Y. D. (2015). Forecasting the 2013–2014 influenza season using Wikipedia. PLoS Comput. Biol. 11 e1004239.
  • Kermack, W. O. and McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. In In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 115 700–721. The Royal Society.
  • Mills, C. E., Robins, J. M. and Lipsitch, M. (2004). Transmissibility of 1918 pandemic influenza. Nature 432 904–906.
  • Nsoesie, E., Mararthe, M. and Brownstein, J. (2013). Forecasting peaks of seasonal influenza epidemics. PLoS Curr. 5.
  • Nsoesie, E. O., Brownstein, J. S., Ramakrishnan, N. and Marathe, M. V. (2014). A systematic review of studies on forecasting the dynamics of influenza outbreaks. Influenza and other Respiratory Viruses 8 309–316.
  • Osthus, D., Hickmann, K. S., Caragea, P. C., Higdon, D. and Del Valle, S. Y. (2017). Supplement to “Forecasting seasonal influenza with a state-space SIR model.” DOI:10.1214/16-AOAS1000SUPP.
  • Plummer, M. (2014). rjags: Bayesian graphical models using MCMC. R package version 3-14.
  • Plummer, M. et al. (2003). JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Proceedings of the 3rd International Workshop on Distributed Statistical Computing 124 125. Vienna.
  • Ross, R. (1911). Some quantitative studies in epidemiology. Nature 87 466–467.
  • Shaman, J. and Karspeck, A. (2012). Forecasting seasonal outbreaks of influenza. Proc. Natl. Acad. Sci. USA 109 20425–20430.
  • Shaman, J., Karspeck, A., Yang, W., Tamerius, J. and Lipsitch, M. (2013). Real-time influenza forecasts during the 2012–2013 season. Nat. Commun. 4 2837.
  • R Core Team (2015). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
  • Towers, S., Chowell, G., Hameed, R., Jastrebski, M., Khan, M., Meeks, J., Mubayi, A. and Harris, G. (2013). Climate change and influenza: The likelihood of early and severe influenza seasons following warmer than average winters. PLoS Curr. 5.
  • U.S. Department of Health and Human Services (2017). Regional Offices. Available at http://www.hhs.gov/about/agencies/regional-offices/. Accessed: 02-06-2017.
  • Weiss, H. H. (2013). The SIR model and the foundations of public health. In Materials Matemàtics 0001–17.
  • Yang, W., Lipsitch, M. and Shaman, J. (2015). Inference of seasonal and pandemic influenza transmission dynamics. Proc. Natl. Acad. Sci. USA 112 2723–2728.

Supplemental materials

  • Supplemental material: Forecasting seasonal influenza with a state-space SIR model. This supplement consists of five parts. Part 1 provides the details of the fourth order Runge–Kutta approximation. Part 2 presents the table of parameter estimates from the regression described in Section 6.5. Part 3 provides the algorithm for sampling from the prior predictive distribution of equation (6.1). Part 4 provides the algorithm for sampling from the posterior predictive distribution of equation (5.2). Part 5 provides MCMC diagnostics for the illustrative forecasting example of Section 7.1.