Former FDA commissioner Dr. Scott Gottlieb said Sunday that infection with COVID-19 variants provide "robust" protection against infection — for awhile at least.

In an interview on CBS News' "Face The Nation," Gottlieb said the protection might not be across all variants.

"What we've seen from the data is that if you get infected with any one of these variants, you probably have a period of immunity that's quite robust," he said.

"We don't know how long it is, but you have a period of immunity that's quite robust and you probably have as good, if not better immunity, against that subsequent variant as if you were just vaccinated and never infected."

According to Gottlieb, the findings mean people who are infected with the delta variant "probably have a pretty robust immunity against delta, and perhaps it's as good, if not better than if they were just vaccinated, never infected with delta."

But he added, the vaccines provide the broadest possible immunity.

"So people with omicron might have good protection against omicron," he noted. "They probably don't have as good protection against delta."

Gottlieb said the omicron variant is now spreading to the Midwest — and coming down quickly in places that were initially hard-hit, including New York and Florida.

"You're seeing cases pick up in states like Montana, Wisconsin, Minnesota, Wyoming, Idaho, so it's not done yet," Gottlieb said. "Across the United States, there's still states that are probably in the thick of this. They have another week, maybe two weeks to go until they peak and start to come down."

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