Research ArticleInfluenza

Evolution-informed forecasting of seasonal influenza A (H3N2)

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Science Translational Medicine  25 Oct 2017:
Vol. 9, Issue 413, eaan5325
DOI: 10.1126/scitranslmed.aan5325
  • Fig. 1. Data and model.

    (A) Monthly influenza incidence data for the United States between October 2002 and June 2016. Red, blue, and green curves are for subtype H3N2, subtype H1N1, and type B, respectively. Seasons with an H3N2 antigenic cluster transition were marked with asterisks. (B) Monthly evolutionary change E(t). E(t) was calculated on the basis of epitope sites of HA, as a weighted sum of normalized amino acid distances (hamming distances) between strains in month t and previous strains. These distances were weighted by a decaying function back in time whose time scale was estimated as part of the model fitting. (C) Diagram for the epidemiological model. A classical SIRS epidemic model was used to represent the population dynamics of H3N2 incidence. Details are described in Materials and Methods.

  • Fig. 2. Best model fits.

    Illustration of the best model fits for the (A) basic, (B) continuous, and (C) cluster models. See Table 1 and main text for the specification and statistical comparison of the different models considered. Here, results from 1000 monthly simulations starting with estimated initial conditions in October 2002 are shown for the respective models with the maximum likelihood estimates parameters, for the median (in red), and for the 95% uncertainty intervals (shaded red, for the 2.5 and 97.5% quantiles of the 1000 runs). For comparison, the observed monthly H3N2 incidence data for the United States are shown in black. The estimated reporting rate and its confidence intervals for both models including virus evolution are given in fig. S11.

  • Fig. 3. H3N2 incidence forecasts based on the cluster model for the Unites States.

    (A) Monthly forecasts and (B) predictions versus observations of seasonal incidence totals. The different colors in both panels correspond to the following: leave-one-out cross-validation (for each influenza season from 2003/2004 to 2010/2011; in blue), retrospective forecasts (for each out-of-fit influenza season from 2011/2012 to 2015/2016; in red), and a real-time forecast for the 2016/2017 influenza season (in green). These predictions for cross-validations are simulated on a seasonal basis from estimated initial conditions starting in June and based on parameters estimated with all the data in the training data set with the target season excluded. The forecasts for the out-of-fit period are also simulated on a seasonal basis from estimated initial conditions starting in June but are based on parameters estimated with all the data up to that point in time. The average monthly H1N1 incidence from this training data set was used for forecasting purposes because the observation of this driver quantity would not be available. Similarly, the quantities specifying the evolutionary change of the virus were extrapolated as the sequences required for their computation would not be available (see Materials and Methods). The black curve is the monthly observed H3N2 incidence; the colored curve is the predicted monthly median incidence with shaded 95% uncertainty intervals (2.5 and 97.5% quantiles) from 1000 random simulations with the best models. The seasonal incidence is the sum of the monthly incidence for a specific influenza season. The observed incidence data for the 2016/2017 influenza season, which were not yet available when this study was conducted, are shown with the dotted line (and based on data from the weekly U.S. influenza surveillance report until week 14 ending on 8 April 2017). There is a significant correlation (P < 0.05) between observed incidence and median incidence, from the cross-validation forecasts for both monthly data (r = 0.66 and r2 = 0.44) and seasonal data (r = 0.88 and r2 = 0.77) and from both the retrospective and real forecasts (r = 0.81 and r2 = 0.67 for monthly data, fig. S4; r = 0.90 and r2 = 0.81 for seasonal data; Pearson’s product moment correlations).

  • Table 1. Model comparison.

    See Fig. 1 for a diagram of the general epidemiological model and the main text for a summary of the different models and their corresponding names used here.

    ModelsEpidemiologyEvolutionNumber parametersAIC
    H1N1α ≠1
    ρwinter & ρsummer
    Seasonal forcingLoss of immunity
    wε ≠ 0
    Transmission
    wβ ≠ 0
    Basic××Periodic splines××144493
    Basic-H1×Periodic splines××174478
    RefinedPeriodic splines××194471
    HumiditySpecific humidity××154484
    Immunity loss/transmissionPeriodic splines224450
    TransmissionPeriodic splines×214458
    Immunity loss (continuous)Periodic splines×214448
    Immunity loss (cluster)Periodic splines×204445
  • Table 2. H3N2 risk level forecasts for the United States based on the cluster model.

    Seasonal risk level for H3N2 influenza virus is defined as high or low for each season compared to a reference level defined as the median of the seasonal total H3N2 incidence cases in the corresponding training data set. We defined an observed season as H3N2 high risk, when the observed total H3N2 incidence surpasses the reference level; and an H3N2 low-risk season otherwise. For the forecasts, the percentage of 1000 simulations that exhibit an H3N2 high risk was obtained. When this percentage exceeded 40% (a level chosen based on fig. S5), we forecasted an H3N2 high-risk season. Otherwise, an H3N2 low-risk season was predicted.

    SeasonsObserved% High
    (1000 simulations)
    Forecasts
    (>40% high)
    2011/2012Low8.2Low
    2012/2013High99.6High
    2013/2014Low3.6Low
    2014/2015High99.9High
    2015/2016Low7.0Low
    2016/2017High*100.0High

    *On the basis of the updated data from the weekly U.S. influenza surveillance report until week 14 ending on 8 April 2017.

    Supplementary Materials

    • www.sciencetranslationalmedicine.org/cgi/content/full/9/413/eaan5325/DC1

      Additional description of materials and methods

      Fig. S1. Illustration of the best model fits for alternative models.

      Fig. S2. Proportion of antigenic variants.

      Fig. S3. ROC curve for predicting antigenic cluster transitions based on the training data set covering the period from 2002 to 2011 in United States.

      Fig. S4. Comparison of monthly observations and forecasts generated with the cluster model for the out-of-fit period covering the period from 2011 to 2017.

      Fig. S5. ROC curve for choosing the percentage cutoff applied to risk level prediction for the cluster model.

      Fig. S6. Forecasts based on the continuous model for the Unites States.

      Fig. S7. Scatter diagram for seasonal simulations and observations for the U.S. data set covering the period from 2002 to 2016 based on the cluster model.

      Fig. S8. H3N2 incidence forecasts for the U.S. HHS region 3.

      Fig. S9. Log-likelihood profiling of the average effective time θ.

      Fig. S10. Log-likelihood profiling of the basic average latent time ε0.

      Fig. S11. Log-likelihood profiling of the reporting rate φ.

      Fig. S12. ROC curve for choosing the percentage cutoff applied to risk level prediction for the continuous model.

      Fig. S13. ROC curves for choosing the percentage cutoff applied to risk level prediction for the U.S. HHS region 3.

      Table S1. H3N2 risk level forecasts based on leave-one-out cross-validation using the cluster model for the period between 2003 and 2011.

      Table S2. Observed and predicted H3N2 seasonal incidence rate for the United States based on the cluster model for the period between 2011 and 2017.

      Table S3. H3N2 risk level forecasts based on the continuous model for the United States.

      Table S4. Model comparison based on data from the U.S. HHS region 3.

      Table S5. H3N2 risk level forecasts for the U.S. HHS region 3.

    • Supplementary Material for:

      Evolution-informed forecasting of seasonal influenza A (H3N2)

      Xiangjun Du, Aaron A. King, Robert J. Woods, Mercedes Pascual*

      *Corresponding author. Email: pascualmm{at}uchicago.edu

      Published 25 October 2017, Sci. Transl. Med. 9, eaan5325 (2017)
      DOI: 10.1126/scitranslmed.aan5325

      This PDF file includes:

      • Additional description of materials and methods
      • Fig. S1. Illustration of the best model fits for alternative models.
      • Fig. S2. Proportion of antigenic variants.
      • Fig. S3. ROC curve for predicting antigenic cluster transitions based on the training data set covering the period from 2002 to 2011 in United States.
      • Fig. S4. Comparison of monthly observations and forecasts generated with the cluster model for the out-of-fit period covering the period from 2011 to 2017.
      • Fig. S5. ROC curve for choosing the percentage cutoff applied to risk level prediction for the cluster model.
      • Fig. S6. Forecasts based on the continuous model for the Unites States.
      • Fig. S7. Scatter diagram for seasonal simulations and observations for the U.S. data set covering the period from 2002 to 2016 based on the cluster model.
      • Fig. S8. H3N2 incidence forecasts for the U.S. HHS region 3.
      • Fig. S9. Log-likelihood profiling of the average effective time θ.
      • Fig. S10. Log-likelihood profiling of the basic average latent time ε0.
      • Fig. S11. Log-likelihood profiling of the reporting rate ϕ.
      • Fig. S12. ROC curve for choosing the percentage cutoff applied to risk level prediction for the continuous model.
      • Fig. S13. ROC curves for choosing the percentage cutoff applied to risk level prediction for the U.S. HHS region 3.
      • Table S1. H3N2 risk level forecasts based on leave-one-out cross-validation using the cluster model for the period between 2003 and 2011.
      • Table S2. Observed and predicted H3N2 seasonal incidence rate for the United States based on the cluster model for the period between 2011 and 2017.
      • Table S3. H3N2 risk level forecasts based on the continuous model for the United States.
      • Table S4. Model comparison based on data from the U.S. HHS region 3.
      • Table S5. H3N2 risk level forecasts for the U.S. HHS region 3.

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