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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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

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

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

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


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.

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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.