An IDEA for short term outbreak projection: nearcasting using the basic reproduction number

Abstract

Background: Communicable disease outbreaks of novel or existing pathogens threaten human health around the globe. It would be desirable to rapidly characterize such outbreaks and develop accurate projections of their duration and cumulative size even when limited preliminary data are available. Here we develop a mathematical model to aid public health authorities in tracking the expansion and contraction of outbreaks with explicit representation of factors (other than population immunity) that may slow epidemic growth.

Methodology: The Incidence Decay and Exponential Adjustment (IDEA) model is a parsimonious function that uses the basic reproduction number R0, along with a discounting factor to project the growth of outbreaks using only basic epidemiological information (e.g., daily incidence counts).

Principal findings: Compared to simulated data, IDEA provides highly accurate estimates of total size and duration for a given outbreak when R0 is low or moderate, and also identifies turning points or new waves. When tested with an outbreak of pandemic influenza A (H1N1), the model generates estimated incidence at the i+1(th) serial interval using data from the i(th) serial interval within an average of 20% of actual incidence.

Conclusions and significance: This model for communicable disease outbreaks provides rapid assessments of outbreak growth and public health interventions. Further evaluation in the context of real-world outbreaks will establish the utility of IDEA as a tool for front-line epidemiologists.

Figure 1. Model fits and “order of control”.

Relationship between final-size-normalized root-mean squared differences (RMSD, Y-axis) between SIR model outputs and IDEA model fits, for R₀ ranging from 1.5 to 7 (legend), with variation in order of control in SIR models (X-axis). It can be seen that for all R₀ best-fits are achieved with first order control. Model fits were however better with low R₀ simulations than with higher R₀ simulations.

Figure 2. IDEA model fits for low R₀ epidemics.

Comparison of prevalent infections and cumulative infections from data generated using the SIR difference equation model described in the text (gray curves), and an IDEA model fitted to the first four generations of the simulated SIR epidemic (dashed curves). The true R₀ used in the SIR model was 3.0. It can be seen that the IDEA model projections reproduce future case counts in the SIR model almost perfectly.

Figure 3. IDEA model fits for higher R₀ epidemics.

Concordance between simulated data from an SIR difference model for a higher-R₀ system (R₀ = 6) (solid gray curves) and IDEA fits based on early (T < = 10) generations (gray dashed curves), and based on fits from generation 15 onwards (black dashed curves). Prevalent infections are shown in the left hand panel while cumulative infections are shown on the right. Fits from generations prior to the epidemic peak (T< = 10) reproduce the initial growth of the epidemic well, and also provide accurate estimates of the true R₀ (R₀∼6.34, d = 0.054); however, these parameters result in IDEA projections of far larger epidemics than actually occur. Once IDEA models are fit using generations that include and follow the epidemic peak (i.e., T> = 15) projections of both prevalent and cumulative infections become fairly accurate (black dashed curves); however, estimated R₀ is much larger than the true value (R₀∼7.56) and the best-fit value for d increases as well (from 0.054 to 0.069).

Figure 4. Model behaviour.

The overall behaviour of the IDEA model based on a range of possible R_o and d values (a) the variation of t_max or outbreak duration as a function of R_o and d (b) the variation of I_total or the final cumulative incidence as a function of R₀ and d.

Figure 5. Pandemic H1N1 case counts modeled with the IDEA Model.

The IDEA model applied to an outbreak of influenza A (H1N1) in Nunavut, Canada, with the model parameters R₀, d, t_max, I_total and Δd. (a) the early stages of the outbreak, with largely exponential growth, (b) dampened growth with reduced projected t_max values by serial interval 7, (c) a second wave in the outbreak and (d) the fit of the model at 24 out of 27 generations.

Figure 6. Utility of the IDEA model in evaluating the impact of public health and social or environmental factors on outbreak behaviour.

(a) The utility of the IDEA model in evaluating the level of control over the outbreak. Each projection is based on the outbreak up to i intervals, projected to the i+1^th interval. With the exception of serial intervals 6 and 7 illustrated in the figure, the projected case counts were less than the actual case counts implying that at each serial interval the outbreak grew more than would be expected by its previous course. During this outbreak, the model underestimated the actual number of cases except during two serial intervals. (b) Percent error between the projection for the next generation and actual case counts according to generation.