Predicting the epidemic sizes of influenza A/H1N1, A/H3N2, and B: a statistical method

Abstract

Background: The epidemic sizes of influenza A/H3N2, A/H1N1, and B infections vary from year to year in the United States. We use publicly available US Centers for Disease Control (CDC) influenza surveillance data between 1997 and 2009 to study the temporal dynamics of influenza over this period.

Methods and findings: Regional outpatient surveillance data on influenza-like illness (ILI) and virologic surveillance data were combined to define a weekly proxy for the incidence of each strain in the United States. All strains exhibited a negative association between their cumulative incidence proxy (CIP) for the whole season (from calendar week 40 of each year to calendar week 20 of the next year) and the CIP of the other two strains (the complementary CIP) from the start of the season up to calendar week 2 (or 3, 4, or 5) of the next year. We introduce a method to predict a particular strain's CIP for the whole season by following the incidence of each strain from the start of the season until either the CIP of the chosen strain or its complementary CIP exceed certain thresholds. The method yielded accurate predictions, which generally occurred within a few weeks of the peak of incidence of the chosen strain, sometimes after that peak. For the largest seasons in the data, which were dominated by A/H3N2, prediction of A/H3N2 incidence always occurred at least several weeks in advance of the peak.

Conclusion: Early circulation of one influenza strain is associated with a reduced total incidence of the other strains, consistent with the presence of interference between subtypes. Routine ILI and virologic surveillance data can be combined using this new method to predict the relative size of each influenza strain's epidemic by following the change in incidence of a given strain in the context of the incidence of cocirculating strains. Please see later in the article for the Editors' Summary.

Figure 1. Weekly incidence proxies of A/H3N2 (green), A/H1N1 (blue), and influenza B (red) strains inferred from .

Figure 2. The relationship between the cumulative complementary incidence for each of the index strains A/H1N1 (A), A/H3N2 (B), and B (C) by epidemiological week 16 (calendar week 3) and the index strain's cumulative incidence over the entire season (i.e., its epidemic size) for the 12 y in the data.

Figure 3. Predicted versus observed values for influenza A/H1N1 for the choice of thresholds h = 140, h _c = 500.

Figure 4. Timing of prediction with regard to weekly influenza A/H1N1 incidence (week 1 = calendar week 40).

Green lines show the stopping time s in seasons in which the index strain's own threshold was crossed first; red lines indicate the stopping times in seasons in which the complementary threshold was crossed first.

Figure 5. Predicted versus observed values for influenza A/H3N2 for the choice of thresholds h = 165, h _c = 350.

Figure 6. Timing of prediction with regard to weekly influenza A/H3N2 incidence (week 1 = calendar week 40).

Green lines show the stopping time s in seasons in which the index strain's own threshold was crossed first; red lines indicate the stopping times in seasons in which the complementary threshold was crossed first.

Figure 7. Predicted versus observed values for influenza B for the choice of thresholds h = 80, h _c = 675.

Figure 8. Timing of prediction with regard to weekly influenza B incidence (week 1 = calendar week 40).

Green lines show the stopping time s in seasons in which the index strain's own threshold was crossed first; red lines indicate the stopping times in seasons in which the complementary threshold was crossed first.