Forecasting seasonal outbreaks of influenza

Abstract

Influenza recurs seasonally in temperate regions of the world; however, our ability to predict the timing, duration, and magnitude of local seasonal outbreaks of influenza remains limited. Here we develop a framework for initializing real-time forecasts of seasonal influenza outbreaks, using a data assimilation technique commonly applied in numerical weather prediction. The availability of real-time, web-based estimates of local influenza infection rates makes this type of quantitative forecasting possible. Retrospective ensemble forecasts are generated on a weekly basis following assimilation of these web-based estimates for the 2003-2008 influenza seasons in New York City. The findings indicate that real-time skillful predictions of peak timing can be made more than 7 wk in advance of the actual peak. In addition, confidence in those predictions can be inferred from the spread of the forecast ensemble. This work represents an initial step in the development of a statistically rigorous system for real-time forecast of seasonal influenza.

Fig. 1.

Results for SIRS-EAKF scheme using model-generated truth plus prescribed observation error variance. (A) Time series of prior and posterior ensemble mean and truth for the susceptible (S) and infected (I) states and the model parameters D (mean infectious period) and R_0max (a transmissibility parameter). Also shown for the infected state are the synthetic observations (truth plus observation error). (B) Time series of prior and posterior ensemble variance for S, I, D, and R_0max.

Fig. 2.

Results for the SIRS-EAKF scheme using weekly GFT estimates of ILI for New York City during the 2004–2005 and 2007–2008 influenza seasons. Two hundred fifty 200-member ensembles were run for each season, each with a different suite of initial conditions. Multiplicative inflation of λ = 1.02 is applied. SIRS model simulations were forced with observed daily specific humidity conditions for New York City. (A) The 2004–2005 influenza season weekly GFT ILI estimates (green) and SIRS-EAKF ensemble mean prior (blue) and ensemble mean posterior (red) of infected (I) averaged for all 250 ensembles. Also shown are the 10th and 90th percentiles of the ensemble posterior I (black lines) averaged for all 250 ensembles. The range between the average 10th and 90th percentiles is shaded gray. (B) Same as A but for the 2007–2008 influenza season.

Fig. 3.

Results for SIRS-EAKF retrospective forecasting using GFT ILI estimates and observed AH conditions for the 2007–2008 season in New York City. Retrospective assimilation began September 2, 2007, and the first forecast occurred after assimilation of the week 1 GFT ILI estimate (representing September 2–8, 2007). Inflation was set at = 1.02. (A–C) Results for a single 200-member SIRS-EAKF run with prediction for 300 d following each assimilation, using the new posterior state and parameter values. (A) Histogram of ensemble forecast peak timing for predictions initiated at the end of weeks 1, 4, 7, 10, 13, 16, 19, 22, 25, and 28 (blue). Also shown are the observed peak (green, week 25) and the ensemble mode (red). Note that the peak for any given ensemble member may occur before the forecast week. (B) Time series of the ensemble mean posterior and spread (blue), the mean prediction and spread (gray), and the observations (green) for predictions initiated at the end of weeks 1, 4, 7, 10, 13, 16, 19, 22, 25, and 28. (C) Time series of the ensemble predicted peak variance log transformed (blue) and percentage of the 200-member ensemble predicting the observed peak (week 25) within ±1 wk (green). Note that for the forecast made the week after the week 25 peak, the percentage of ensemble members accurately predicting the peak drops as some ensemble members erroneously forecast still more infections in the future; however, after 2 wk of continued decline in GFT observations the forecasts “recognize” the abatement and no longer forecast any future resurgence of infection. (D) Percentage of the 200-member ensemble predicting the peak within ±1 wk of the actual peak (week 25) for each weekly prediction (weeks 1–28) for each of 250 SIRS-EAKF assimilation runs plotted as a function of the ensemble predicted peak variance log transformed. Each of the two hundred fifty 200-member SIRS-EAKF assimilation runs was initiated with a different suite of initial state and parameter combinations. Color coding denotes the week the prediction was made relative to the actual week 25 peak: 10 wk or more prior (blue), 7–9 wk prior (green), 4–6 wk prior (red), 1–3 wk prior (cyan), and on or after the peak (black).

Fig. 4.

Results for SIRS-EAKF retrospective forecasting using GFT ILI estimates for the 2003–2004 through 2008–2009 seasons in New York City. Retrospective assimilations began in either August or October. Two hundred 200-member SIRS-EAKF assimilations were performed for each season and each of these start months, excepting 2003–2004 for which only October was run as August 2003 GFT ILI estimates are unavailable. Inflation was set at = 1.02. Forecasts were run for 300 d following each assimilation, using the new posterior state and parameter values. The forecasts are grouped using 0.25-wk squared bins of ensemble predicted peak variance log transformed. The proportions of ensemble mode predicted peak within each bin that are within ±1 wk of the observed GFT ILI estimate for that season are plotted as a function of the ensemble predicted peak variance log transformed. The different subplots group the predictions by lead time; i.e., “4–6 wk in the future” indicates the forecast mode, whether correct or not, was predicted to be 4–6 wk in the future. The different color lines are for (i) the first forecast form, 5 d of true AH conditions followed by daily 1979–2002 AH climatology and full EAKF constraint (red); and (ii) the second forecast form, AH as in the first form but no EAKF constraint of model parameters and the susceptible variable (green).