Estimation of the reproductive number and the serial interval in early phase of the 2009 influenza A/H1N1 pandemic in the USA

Abstract

Background: The United States was the second country to have a major outbreak of novel influenza A/H1N1 in what has become a new pandemic. Appropriate public health responses to this pandemic depend in part on early estimates of key epidemiological parameters of the virus in defined populations.

Methods: We use a likelihood-based method to estimate the basic reproductive number (R(0)) and serial interval using individual level U.S. data from the Centers for Disease Control and Prevention (CDC). We adjust for missing dates of illness and changes in case ascertainment. Using prior estimates for the serial interval we also estimate the reproductive number only.

Results: Using the raw CDC data, we estimate the reproductive number to be between 2.2 and 2.3 and the mean of the serial interval (mu) between 2.5 and 2.6 days. After adjustment for increased case ascertainment our estimates change to 1.7 to 1.8 for R(0) and 2.2 to 2.3 days for mu. In a sensitivity analysis making use of previous estimates of the mean of the serial interval, both for this epidemic (mu = 1.91 days) and for seasonal influenza (mu = 3.6 days), we estimate the reproductive number at 1.5 to 3.1.

Conclusions: With adjustments for data imperfections we obtain useful estimates of key epidemiological parameters for the current influenza H1N1 outbreak in the United States. Estimates that adjust for suspected increases in reporting suggest that substantial reductions in the spread of this epidemic may be achievable with aggressive control measures, while sensitivity analyses suggest the possibility that even such measures would have limited effect in reducing total attack rates.

Figure 1

Confirmed and probable cases in the United States plotted by onset time. First date of onset is March 28, 2009.

Figure 2

(A) Reporting delay by the date of report. (B) Imputed data and original data. (C) All data (right frame), (D) only augmented data where at least 5% of the data is observed.

Figure 3

Serial interval estimates for k = 4, 5, 6, and 7 days with −log(likelihood) values.

Figure 4

Estimates for the reproductive number, mean, and variance of the serial interval. The results using the original data (solid line), imputed data (dashed line), and augmented data (dotted line) are all shown using data with onset date no later than the value in the x‐axis. Augmented data estimates are not shown after April 30, 2009 since less than 5% of the data is original data. These results correspond, in part to those shown in Table 1. The fourth pane shows the contour plot of the joint density estimate of the mean of the serial interval and the basic reproductive number for imputed data up to and including April 27. The values of the contours correspond the estimated 25th, 50th, 75th, and 97·5th percentiles of the joint density.

Figure 5

Serial interval estimate using data up to and including 4/25/2009 (top figure), 4/26/2009 (second), 4/27/2009 (third), and 4/28/2009 (bottom figure).