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Control (CDC) providing information on all early reported cases in the United States, including the date of symptom onset and report. Further, we illustrate the impact of the reporting fraction and temporal trends in the reporting fraction on estimates of these parameters.

Methods

Data

We use data from the Centers for Disease Control and Prevention (CDC) line list of reported cases of influenza A/H1N1 in the United States beginning on March 28, 2009. Information about 1368 confirmed and probable cases with a date of report on or before May 8, 2009 was used. Of the 1368 reported cases, 750 had a date of onset recorded. We include probable cases in the analysis as >90% of probable cases subsequently tested have been confirmed. After May 13 collection of individual-based data became much less frequent and eventually halted in favor of aggregate counts of new cases. The degree of case ascertainment early throughout this time period is unknown.

Statistical Analysis

We make use of the likelihood-based method of White and Pagano (White and Pagano, 2008a,b). This method is well suited for estimation of the basic reproductive number, R0, and the serial interval in real time with observed aggregated daily counts of new cases, denoted by N = {N0, N1,…, NT}, where T is the last day of observation and N0 are the initial number of seed cases that begin the outbreak. The Ni are assumed to be composed of a mixture of cases that were generated by the previous k days, where k is the maximal value of the serial interval. We denote these as Xji, the number of cases that appear on day i that were infected by individuals with onset of symptoms on day j. We assume that the number of infectees generated by infectors with symptoms on day , follows a Poisson distribution with parameter R0Nj. Additionally, Xj = {Xj,j + 1, Xj,j + 2,…, Xj,j+ k + 1}, the vector of cases infected by the Nj individuals, follows a multinomial distribution with parameters p, k and Xj. Here p is a vector of probabilities that denotes the serial interval distribution. Using these assumptions, we obtain the following likelihood, as shown in White and Pagano (2008b):

where and Γ(x) is the gamma function. Maximizing the likelihood over R0 and p provides estimators for the reproductive number and serial interval. This method assumes that there are no imported cases, there is no miss-



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