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Dr. Anthony Fauci got into a contentious exchange with Sen. Rand Paul (R-KY) Thursday over whether people should wear masks if they have recovered from Covid-19 or been vaccinated against it.

Paul, who says he has been infected with coronavirus and who pointedly refuses to wear a mask, attacked Fauci during a hearing of the Senate Health, Education, Labor and Pensions Committee.

"You're telling everybody to wear a mask, whether they've had an infection or a vaccine," Paul said to Fauci, who is director of the National Institute of Allergy and Infectious Diseases. "If people that have had the vaccine or have had the infection ... if we're not spreading the infection, isn't it just theater?" Paul asked.

"Here we go again with the theater. Let's get down to the facts," Fauci replied. "Let me just state for the record that masks are not theater. Masks are protective."

Fauci has noted before that people who are vaccinated may still breathe in virus, have it living in their nose or throat without causing an infection, and breathe, cough or sneeze infectious virus onto others. People can also become re-infected after they've recovered, although it is uncommon.

The Centers for Disease Control and Prevention says people who have been vaccinated should nonetheless still wear masks when around people who are not vaccinated.

"And you don't keep in the concept of variants. That's an entirely different ballgame," Fauci added.

"That's a good reason for a mask."

Asked about the exchange by CNN's Chris Cuomo on "Prime Time" Thursday evening, Fauci said, "I don't know what he believes, to be honest with you."

"I've been dealing -- this is not the first time we've clashed at a Senate hearing. You know, there is always -- as is always the case -- a kernel of truth in what he says about that there is protection to some extent after you get infected, there's no doubt about that," Fauci continued.

"He completely does not take into account the variants."

New variants of the virus, such as the B.1.1.7 variant first seen in Britain and the B.1.351 variant first seen in South Africa, are spreading more widely and may elude the immune response prompted by a previous infection. Fauci noted at the hearing at least one study showed people in South Africa who had been infected with older strains of coronavirus had almost no immune protection against B.1.351.

"You're not hearing what I am saying about variants," Fauci said during the hearing.

"You've been vaccinated and you parade around in two masks for show," responded Paul, who is an ophthalmologist. "You want people to get the vaccine, give them a reward instead of telling them that the nanny state is going to be there for three more years and you got to wear a mask forever. People don't want to hear it."

"I totally disagree with you," Fauci said.

The nation's leading infectious disease expert said Thursday evening that his concern with Paul's approach is that people will follow his lead in not wearing a mask after being infected with the virus.

"If people hear what he says, and believe it, and you have an elderly person who has been infected, and they decide, well, Rand Paul says, 'Let's not wear a mask,' they won't, " Fauci said.

"They could get reinfected again and get into trouble," he added. "So that's the thing that bothers me about that type of an interchange."