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That assumption turned out to be more optimistic about the program’s numbers than turned out to be case - about 6.8 million doses were available and 3.7 million doses had been ordered, the CDC said on Oct. 9.

Shipments reported Friday were down by a quarter, because of a slowdown in production caused by difficulties of processing great numbers.

The study also assumed that all adults would achieve full immunity shortly after receiving inoculations and assumed that children and adults are equally responsive to the flu vaccine. Both assumptions are medically dubious, though hard to compensate for statistically.

All these statistical assumptions and prediction errors would lead the study to underestimate the number of infections.

The study was based on a statistical analysis of weekly reports from the CDC for a model derived from the observed spread of the H1N1 virus “during summer 2009 to predict the behavior of the pandemic during autumn 2009.”

A White House scenario released in late August by a group of presidential advisers had predicted that anywhere from 30 percent to 50 percent of the population would get the novel virus strain, and an estimate on the number of deaths ranged from 30,000 to 90,000. The regular seasonal flu normally affects up to 20 percent of the population, with 36,000 deaths resulting.

Dr. Thomas Frieden, CDC director, cautioned at the time that such a prognosis was unlikely unless the virus changed and mutated into another form, which, to date, has not happened. Further estimates and availability of vaccine doses are due from CDC officials Tuesday.

But the Purdue scholars’ study predicts a higher rate of infection and illness than previous projections because, the authors explained to The Washington Times in separate e-mails, they used a better formula - “a seasonally forced SIR model” that adjusts the rates of infection spread for the different times of the year.

“However, one aspect of influenza that needs to be added to the [SIR] model is its seasonal nature; it is more infectious in the fall and winter in the northern hemisphere than it is in the summer. We refer to this as ‘seasonal forcing.’ … Our model takes this seasonal forcing into account,” Ms. Towers wrote.