A day after President Biden issued broad vaccine mandates aimed at propelling American workers to get vaccinated against the coronavirus, federal health officials released a handful of studies highlighting how effective the shots are at preventing infections, hospitalizations and deaths — even while the highly contagious Delta variant has been dominant.

Three studies that drew data from different U.S. regions evaluated the protective power of the vaccines. One looked at more than 600,000 virus cases in 13 states, representing about one quarter of the U.S. population, between April and July, and concluded that individuals who were not fully vaccinated were far more susceptible to infection and death from the virus.

They were 4.5 times more likely than vaccinated individuals to become infected, 10 times more likely to be hospitalized, and 11 times more likely to die from the coronavirus, the study found.

Vaccine protection against hospitalization and death remained strong even when the Delta variant was the dominant form of infection. But the vaccines’ effectiveness in preventing infection dropped from 91 percent to 78 percent, the study found.

The studies underscore a series of similar findings in recent weeks.

“As we have shown, study after study, vaccination works,” said Dr. Rochelle Walensky, the director of the Centers for Disease Control and Prevention, at a White House Covid briefing on Friday.

As more and more Americans become vaccinated, experts always expected that immunized people would represent a greater percentage of hospitalized patients. “What I want to reiterate here is it’s still well over 90 percent of people who are in the hospital who are unvaccinated,” Dr. Walensky said.

“We still have more than 10 times the number of people in the hospital who are unvaccinated, compared to vaccinated,” she added.

Two other studies published on Friday detected waning protection from the vaccines among older adults.

One study, conducted at five Veterans Affairs Medical Centers, found that protection against hospitalization declined with age, to 80 percent for those aged 66 and older, down from 95 percent for adults aged 18 to 64. A second study found vaccine effectiveness dropped off at age 75.

The findings could help identify populations who may be in need of additional doses or booster shots. In August, the Food and Drug Administration authorized giving third doses of Pfizer-BioNTech’s and Moderna’s coronavirus vaccines for some people with weakened immune systems, including organ transplant patients.

But officials have said there is insufficient data on whether the vaccines’ effectiveness declines over time to recommend boosters for healthy adults.

The data also suggests that the Moderna vaccine may be slightly more effective at preventing infections and hospitalizations with the Delta variant, compared with the Pfizer-BioNTech vaccine. Both of the mRNA vaccines had higher efficacy rates than the Johnson & Johnson shot, but the studies were not originally designed to evaluate the comparative effectiveness of different vaccinations.

In the study of 33,000 medical encounters in nine states between June and August, the Moderna vaccine had an effectiveness rate of 92 percent against infection, compared with 77 percent for the Pfizer-BioNTech shot.

Sharon LaFraniere contributed reporting from Washington.

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