High-profile "breakthrough" Covid cases, from an aide to House Speaker Nancy Pelosi to U.S. gymnast Kara Eaker to several Yankees, are raising questions about what a positive test means for those who are fully vaccinated.

The Centers for Disease Control and Prevention only counts breakthrough cases that lead to hospitalizations and deaths: Since July 12, it's documented 5,492 such patients (the majority of whom are over the age of 65) out of the more than 160 million people in the U.S. who have been fully vaccinated.

Still, breakthrough cases are not something to ignore, especially with the more transmissible and dangerous delta variant now accounting for 83% of all sequenced Covid cases in the U.S.

"We are concerned that we are seeing more so-called breakthrough infections," Dr. Anthony Fauci, White House chief medical advisor told CNBC's Sara Eisen on "Closing Bell" Wednesday. "That's something we obviously don't want to see we're dealing with a highly transmissible virus."

That's because any case of Covid can continue the spread of Covid and its variants, says Dr. Iahn Gonsenhauser, chief quality and patient safety officer at The Ohio State University Wexner Medical Center.

"If you're vaccinated and have a breakthrough positive case, you want to limit your exposure to others so that we can limit the capacity that the viral variants have both to spread and to continue to mutate," Gonsenhauser says.

Here's what you need to know:

What happens when you get a 'breakthrough' infection

Breakthrough infections are to be expected with any vaccine. Fortunately, breakthrough Covid cases tend to be mild and asymptomatic.

Even with regards to the delta variant, most fully vaccinated people who test positive don't have symptoms, the World Health Organization said July 13.

And vaccinated people who get infected tend to have a level of virus in their nasal pharynx that is "considerably less than ... a person who is infected, unvaccinated and asymptomatic," Fauci said during a White House briefing Friday.

What to do if you test positive but are fully vaccinated

If a vaccinated person tests positive for Covid, through routine workplace testing, for example, "we don't just let them go about their business and forget about the fact that they tested positive," says Dr. Peter Katona, professor of medicine and public health at UCLA and chair of the Infection Control Working Group.

"With the understanding that you're less of a problem than an unvaccinated [person], it doesn't mean you let up on your protocol," he says.

The most important thing to do after testing positive would be to isolate, meaning you stay away from people who are not sick, including others who are vaccinated, and monitor for Covid-related symptoms, Gonsenhauser says.

"You are going to have to isolate just as though you were not vaccinated for 10 days from the first symptoms that you recognize or from the time of your test...keeping yourself from being around other people until that period is up," Gonsenhauser says.

You should avoid visiting any private or public areas or traveling during that 10-day period, according to the CDC.

Just as prior to getting vaccinated, you should notify anybody who you've been in direct contact with without a mask for 15 minutes or more that you have tested positive, he says.

If you come in contact with someone with a breakthrough infection

The CDC updated its guidance for vaccinated people on July 28, adding that even fully vaccinated people should get tested for Covid three to five days after a known exposure, regardless of their symptoms. People who are exposed should also wear masks in public indoor spaces for 14 days after exposure until a negative test is confirmed.

(Before, the CDC said most fully vaccinated people who have been exposed to someone who has Covid-19 but have no Covid-like symptoms themselves don't need to quarantine, stay home from work or even get tested.)

New data suggests that people who get breakthrough infections can transmit Covid to other people.

If a vaccinated person in your household tests positive for Covid, "you want to be as practical as you can," Katona says. "Try to limit the contact with other people in the household as much as possible," he says.

That's "unless you were to develop symptoms," Gosenhauser says.

The CDC says that fully vaccinated people who experience Covid symptoms — fever or chills, cough and shortness of breath — should isolate themselves, be evaluated for Covid-19 by a doctor or healthcare provider and get tested.

Correction: This story was revised to correct that an aide to Rep. Nancy Pelosi was diagnosed with breakthrough Covid.

This story was updated to include new testing guidelines from the CDC about fully vaccinated people who are exposed to Covid.

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