Swine flu has sickened about 22 million Americans since April and killed nearly 4,000, including 540 children, say startling federal estimates released Thursday.

The figures — a quadrupling of previous death estimates — don’t mean swine flu suddenly has worsened, and most cases still don’t require a doctor’s care. Instead, the numbers are a long-awaited better attempt to quantify the new flu’s true toll.

“I am expecting all of these numbers, unfortunately, to continue to rise,” said Dr. Anne Schuchat of the Centers for Disease Control and Prevention. “We have a long flu season ahead of us.”

Tight supplies of vaccine to combat the illness continue: Not quite 42 million doses are currently available, a few million less than CDC had predicted last week.

A new Associated Press-GfK poll shows nearly one in six parents has gotten at least some of their children vaccinated against swine flu since inoculations began last month. Another 14 percent of parents sought vaccine, but couldn’t find any.

Only about 30 percent of children routinely get flu vaccinations during a normal winter. That even this many have gotten vaccinated against the new flu that scientists call the 2009 H1N1 strain despite the shortage suggests CDC’s target-the-young message has gotten through.

Three times as many adults have tried and failed to find vaccine for themselves as have succeeded.

“I know they’re trying their hardest,” Joy McGavin of Pittston, Pa., said of the CDC’s vaccine efforts. She hasn’t yet found vaccine for her three children despite a persistent hunt — even though she and her youngest child are at extra risk because of chronic illnesses.

“But it is kind of frustrating, being as my children’s school already shut down” because of a big outbreak, McGavin said.

Interest among the young adults who also are at high risk is waning fast, found the AP-GfK poll of 1,006 adults nationwide.

Thursday, Schuchat again urged patience in seeking vaccine.

“It’s a marathon and not a sprint,” she said. “More vaccine is being ordered and delivered and used every day.”

Until now, the CDC has conservatively estimated more than 1,000 deaths and “many millions” of new H1N1 infections. The agency was devoting more time to battling the pandemic than to counting it, and earlier figures were based on laboratory-confirmed cases even as doctors largely quit using flu tests months ago — and experts knew that deaths from things like the bacterial pneumonia that often follows flu were being missed.

Thursday’s report attempts to calculate the first six months of the new H1N1 strain’s spread, from April through mid-October. The CDC said:

— Some 98,000 people have been hospitalized from this new flu or its complications, including 36,000 children, 53,000 adults younger than 65 and 9,000 older adults.

— Deaths could range from a low of 2,500 to as many as 6,100, depending on how the data’s analyzed.

— Some 8 million children have become ill, 12 million adults younger than 65 and 2 million older adults.

The estimate of child deaths may seem especially surprising, considering the CDC’s conservative count of lab-confirmed deaths a week ago was 129.

“We don’t think things have changed from last week to this week,” Schuchat stressed, explaining the importance of looking beyond those lab counts. It’s “a better estimate for the big picture of what’s out there.”

The question now is what effect those estimates will have on a public that largely views swine flu as not that big a threat.

The AP-GfK poll, conducted last weekend, found just 23 percent of responders — and 27 percent of parents — were very likely to keep seeking vaccine.

Stephanie Hannon of Douglas, Mass., decided to get a swine flu vaccine for just one of her three children, the one at extra risk because of asthma. She’s concerned that the swine flu vaccine hasn’t been studied long enough to justify for her less-at-risk youngsters.

“Only because of my other daughter’s condition, I felt like I didn’t have a choice,” she said. “You never know if you make the right decision.”

Swine flu targets young adults, too, yet just 16 percent of 18- to 29-year-olds were very likely to seek vaccine, down from 34 percent in September.

The AP-GfK Poll was conducted November 5-9 by GfK Roper Public Affairs and Media. It involved landline and cell phone interviews with 1,006 adults nationwide, and has a margin of sampling error of plus or minus 3.1 percentage points.