A wedding in Oklahoma leads to 15 vaccinated guests becoming infected with the coronavirus. Raucous Fourth of July celebrations disperse the virus from Provincetown, Mass., to dozens of places across the country, sometimes carried by fully vaccinated celebrants.

As the Delta variant surges across the nation, reports of infections in vaccinated people have become increasingly frequent — including, most recently, among at least six Texas Democrats, a White House aide and an aide to Speaker Nancy Pelosi.

The highly contagious variant, combined with a lagging vaccination campaign and the near absence of preventive restrictions, is fueling a rapid rise in cases in all states, and hospitalizations in nearly all of them. It now accounts for about 83 percent of infections diagnosed in the United States.

But as worrying as the trend may seem, breakthrough infections — those occurring in vaccinated people — are still relatively uncommon, experts said, and those that cause serious illness, hospitalization or death even more so. More than 97 percent of people hospitalized for Covid-19 are unvaccinated.

“The takeaway message remains, if you’re vaccinated, you are protected,” said Dr. Celine Gounder, an infectious disease specialist at Bellevue Hospital Center in New York. “You are not going to end up with severe disease, hospitalization or death.”

Reports of breakthrough infections should not be taken to mean that the vaccines do not work, Dr. Anthony S. Fauci, the Biden administration’s top pandemic adviser, said on Thursday at a news briefing.

“By no means does that mean that you’re dealing with an unsuccessful vaccine,” he said. “The success of the vaccine is based on the prevention of illness.”