ATLANTA – As many as 5.7 million Americans were infected with H1N1 flu during the first few months of the pandemic, according to estimates from federal health officials.

Scientists at the Centers for Disease Control and Prevention estimate that between 1.8 million and 5.7 million Americans were infected from mid-April through July 23. The figures are the CDC’s most specific calculation to date.

They also estimated that between 9,000 and 21,000 hospitalizations occurred during that time. The estimates are in a CDC publication, Emerging Infectious Diseases, and were posted on the journal’s Web site this week.

To come up with the numbers, the scientists assumed that most people infected with H1N1, also called swine flu, had only mild illnesses and did not get medical care or get tested. For every confirmed case, they estimated 80 others occurred. And for every confirmed hospitalization, there were probably three others.

Rates of testing and hospitalization have dropped since the pandemic began, so the same calculation couldn’t be done for cases since late July.

For that reason, CDC officials are saying simply that “many millions” of Americans have been infected to date, the CDC’s Dr. Anne Schuchat said Thursday.

Schuchat also provided an update on a shortage of the children’s version of the drug Tamiflu, a first-line H1N1 treatment. The shortage first emerged last month. Since then, the federal government has released 300,000 pediatric Tamiflu doses to the states from a national medicine stockpile.

The shortage occurred because the drug’s manufacturer, Switzerland-based Roche Holdings, decided to focus production on adult-strength capsules as it dealt with increasing demand for the medication.

There are scattered shortages of pediatric doses, but adult-strength Tamiflu pills are in good supply and pharmacies can turn them into a Tamiflu syrup for children, said Schuchat, who heads the CDC’s National Center for Immunization and Respiratory Diseases.