Seasonal Influenza Forecasting in Real Time Using the Incidence Decay With Exponential Adjustment Model

Abstract

Background: Seasonal influenza epidemics occur frequently. Rapid characterization of seasonal dynamics and forecasting of epidemic peaks and final sizes could help support real-time decision-making related to vaccination and other control measures. Real-time forecasting remains challenging.

Methods: We used the previously described "incidence decay with exponential adjustment" (IDEA) model, a 2-parameter phenomenological model, to evaluate the characteristics of the 2015-2016 influenza season in 4 Canadian jurisdictions: the Provinces of Alberta, Nova Scotia and Ontario, and the City of Ottawa. Model fits were updated weekly with receipt of incident virologically confirmed case counts. Best-fit models were used to project seasonal influenza peaks and epidemic final sizes.

Results: The 2015-2016 influenza season was mild and late-peaking. Parameter estimates generated through fitting were consistent in the 2 largest jurisdictions (Ontario and Alberta) and with pooled data including Nova Scotia counts (R₀ approximately 1.4 for all fits). Lower R₀ estimates were generated in Nova Scotia and Ottawa. Final size projections that made use of complete time series were accurate to within 6% of true final sizes, but final size was using pre-peak data. Projections of epidemic peaks stabilized before the true epidemic peak, but these were persistently early (~2 weeks) relative to the true peak.

Conclusions: A simple, 2-parameter influenza model provided reasonably accurate real-time projections of influenza seasonal dynamics in an atypically late, mild influenza season. Challenges are similar to those seen with more complex forecasting methodologies. Future work includes identification of seasonal characteristics associated with variability in model performance.

Keywords: epidemics; epidemiology; forecasting; influenza; mathematical modeling.

Figure 1.

Weekly incidence of influenza cases in Ottawa, Ontario, Alberta, and Nova Scotia. The vertical axis represents the number of influenza cases reported by participating laboratories and Ottawa Public Health, covering the period between week 48 (beginning November 23, 2015) and week 21 (beginning May 23, 2016).

Figure 2.

Parameter estimates, summed provincial case counts. Parameter estimates (solid lines; R₀: left y-axis, and d: right y-axis) for summed influenza counts from Ontario, Alberta, and Nova Scotia. Dashed lines represent 95% confidence intervals for parameter estimates. Overall influenza activity had begun in late November 2015; parameter estimates had stabilized by mid-January 2016. The dates on the x-axis represent the date of the most recent influenza data used for model fitting.

Figure 3.

Final size projections for 2015–2016 influenza season. Projections of final epidemic size generated using the incidence decay with exponential adjustment (IDEA) model for summed influenza counts from Ontario, Alberta, and Nova Scotia (y-axis). The dates plotted on the x-axis are the dates of most recent influenza data used for model fitting. The solid black line represents projected size; dashed black lines represent upper- and lower-bound 95% confidence intervals (CIs). Upper-bound CI for final size before February 2016 are >100000 and not shown on the graph. Dashed gray line represents true final size (11686 cases).

Figure 4.

Peak date projections for 2015–2016 influenza season. Projections of final epidemic peak date generated using the incidence decay with exponential adjustment (IDEA) model for summed influenza counts from Ontario, Alberta, and Nova Scotia. The dates plotted on the x-axis are the dates of most recent influenza data used for model fitting; the y-axis represents the projected peak date. As noted in the text, peak date projections stabilized in mid-February before the true peak (first week of March 2016). Thus, a stable peak date was forecast before the true peak, but this forecast was persistently earlier than the true peak date.