Landscape architect Scheri Fultineer walked out of the white vaccination tent at Massachusetts General Hospital with a Band-Aid on her shoulder and a feeling of delight at how easy it was. “Earlier in the year,” she said, “I was not optimistic.”

In mid-February, just as eligibility expanded to everyone 65 and older, the state’s sign-up website crashed, so infuriating Gov. Charlie Baker that he publicly fumed: “My hair’s on fire.”

Across the U.S., such out-of-the-gate stumbles have been righted and then some. Massachusetts’ vaccine effort is moving so quickly that almost 38% of residents have received at least one dose, and the massive new system for getting shots into arms has plenty of untapped capacity.

“We could double our vaccination rate without too much effort,” said Paul Biddinger, a physician and chair of the state’s vaccine advisory committee.

Nationwide, vaccinations hit a seven-day average of more than 3 million a day last weekend, and the country logged a 4-million-shot Saturday. (On Monday, the daily vaccination count plummeted to 2.1 million, but the drop was an expected anomaly after a holiday weekend.)

“Quite a turnaround,” tweeted medical researcher and author Eric Topol. “Who would ever have thought that the same country that couldn’t even get a COVID test working and scalable for two months could vaccinate more than 4 million people in a day?”

More than 100 million Americans have gotten at least one dose, according to the U.S. Centers for Disease Control and Prevention, close to a third of the population. The daily rates are expected to rise further as vaccine-makers deliver a promised 700 million doses by the end of July.

The threshold for herd immunity is estimated at about three-quarters of the population; at the current rate, it could be achieved in three months, according to the Bloomberg Vaccine Tracker.

People prepare COVID-19 vaccines at an old TJ Maxx store used by the Lynchburg Fire Department as a mass COVID-19 vaccination site in Lynchburg, Virginia, on March 13. | AFP-JIJI
People prepare COVID-19 vaccines at an old TJ Maxx store used by the Lynchburg Fire Department as a mass COVID-19 vaccination site in Lynchburg, Virginia, on March 13. | AFP-JIJI

The pace has been accelerating in recent weeks. This winter, the country took five weeks to go from an average of 1 million daily shots to 2 million shots, hampered by limited early supply and bad weather. It took only four weeks to hit the current average of more than 3 million shots a day.

Almost half of U.S. states had opened vaccinations to everyone 16 and older by the end of last week. That will rise to 36 by the end of this week. All 50 have now committed to opening eligibility to all adults by May 1, President Joe Biden’s goal. The administration will now accelerate that benchmark to April 19, a White House official said Tuesday morning, asking to remain anonymous ahead of the announcement.

It remains to be seen whether the vaccination campaign can outrace new virus variants, but racing it is.

In New York City, more than 450 vaccination sites are now scattered through the five boroughs, an infrastructure so extensive that the city can inoculate half a million people a week if it has the supply. The locations — including a network of clinics and 24-hour centers, not to mention Yankee Stadium — are so plentiful that they’ve been attracting many vaccine-seekers from outside the city.

In Washington state, delivery has been going so well that eligibility will open to the general population over 16 in mid-April, two weeks earlier than initially planned.

And in Los Angeles, Andrew Friedman, a resident who created an alert service that gives Twitter followers updates on when and where they can get shots, said he’s seen sites with appointments available rise from just a couple to 37 on a recent day.

Those represented thousands of possible slots just as Los Angeles County was expanding its availability to those 50 and over on Thursday, and to anyone 16 and over on April 15. “It’s much easier to get an appointment,” Friedman said. “A lot more doses are coming out, and it’s getting a lot smoother.”

So after some initial efforts went embarrassingly wrong, what’s now going right?

First, “We got the supply of the vaccine flowing through the system,” said Robert Huckman, faculty chair of the Health Care Initiative at Harvard Business School. “That’s probably the biggest driver of our ability to expand the number of shots given each day.”

The next-most-important factor, Huckman said, is the addition of many more places for giving the shots, including “bigger channels.” Massachusetts, for example, has seven mass-vaccination sites, including Gillette Stadium, where the New England Patriots play football.

“Massachusetts embraced mass vaccination early,” said Tim Rowe, chief executive officer of CIC Health, which is running those megasites. Its parent company, idled by the pandemic, applied its experience developing real estate for tech and biotech companies to set up the spaces, he said.

“We were the kids on the block that had the time and the expertise,” from logistics to licensing and handling visitors, Rowe said. “It’s basic stuff that you have to do well.”

Breakneck efforts around the country to construct mass-vaccine sites yielded some initial failures, Rowe said, but “that was the learning curve.”

In Texas, 28% of the population has gotten at least one dose, close to the national rate, and the state received a supply of 2.5 million doses this week, the most ever.

The Massachusetts megasites have given more than half a million shots. Hospitals and pharmacies combined have given more than three times as many, the latest state figures show.

“The hospitals have really done a ton of vaccinations,” said Biddinger of the advisory council. “We are really fortunate to have extraordinary health care infrastructure.”

Community health centers and local health departments are also pitching in. And when it comes to helping people sign up for their shots, even private individuals have been contributing — shepherding individuals through sign-ups or creating do-it-yourself software tools for grabbing a slot.

A health care worker administers a dose of the Johnson & Johnson COVID-19 vaccine to a senior resident at Rotary Valley Senior Village in San Rafael, California, on March 25. | BLOOMBERG
A health care worker administers a dose of the Johnson & Johnson COVID-19 vaccine to a senior resident at Rotary Valley Senior Village in San Rafael, California, on March 25. | BLOOMBERG

For now, demand for vaccines remains greater than supply. But “some time in the next two months, supply is going to be greater than demand,” Biddinger said, and that is what he worries about most.

It would be great if at least 60% of the population could be vaccinated before “we’re really starting to beat the bushes,” he said. “But to get to 70- or 80-plus percent is going to be hard. And we really have to understand everybody’s reasons for hesitancy, and we have to be able to address them and we have to get past them.”

Recent polls find rising acceptance of the vaccines in the U.S.: 75% are willing to get the shots, up from 67% in late January, according to AP-NORC polling.

“What about that last quarter?” said Rowe of CIC Health. “There’s a lot of work going into thinking about the stragglers.”

States have also been ramping up efforts for equity, he said, trying to provide more access in disadvantaged neighborhoods. On average, states have vaccinated more than a quarter of their white populations but only around 1 in 7 Black people and 1 in 8 Hispanic residents, according to a demographic analysis by Bloomberg.

This week, a new Federal Emergency Management Agency megasite in a central Boston convention complex is slated to give 7,000 shots a day, particularly to people from nearby communities of color.

New York City officials have said they would intensify vaccination in minority and immigrant neighborhoods, though gaps remain. For instance, Black people make up 24% of the city’s population but 20% of those vaccinated with at least one shot.

Even as vaccine numbers climb, so do the cases of more contagious variants. At UMass Memorial Medical Center in Worcester, most COVID-19 cases these days involve a new strain, epidemiologist Richard Ellison told Bloomberg Radio.

As accountant Laureen Sava made her way out of the Massachusetts General vaccination tent in Boston, though, she said she was feeling like the state and the country are getting ahead of the curve, that, “We’re going to beat any variants out there.”

She is “not a Democrat,” she said, but the current administration’s vaccination push inspires confidence to the point that she has a hopeful new slogan: “Travel 2022.”

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