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Former Food and Drug Administration Scott Gottlieb clarified some important points about the coronavirus and potential immunity during the latest edition of CBS News' Face the Nation on Sunday.

The Centers for Disease Control and Prevention recently updated its guidance, which now says people who have recovered from COVID-19 don't need to quarantine or get tested for at least three months. Gottlieb said it's likely "sterile immunity" lasts even longer, probably varying by individual between "six to 12 months," but because the virus is new, the data needed to confirm the hypothesis doesn't exist yet.

Gottlieb was less optimistic about "herd immunity," which most scientists agree settles in at around a 60 percent infection rate within a community. He said he believes the U.S. is somewhere around 8 percent nationally, while places like New York, Florida, and Texas are almost certainly higher, albeit a long way off from the target number. Still, herd immunity is not an all or nothing concept, he suggested. In New York City, for instance the 20 percent infection rate shown in seroprevalence studies should still help slow transmission rates going forward.

Lastly, Gottlieb spoke briefly about the speculation surrounding T-cell immunity, which is separate from the more frequently-discussed antibodies. Research has suggested people may have residual protection from prior exposure to other coronaviruses that cause the common cold. While it's too early to prove that for sure, Gottlieb said, if it is the case, T-cells will probably help fight off COVID-19, the disease, but won't prevent a coronavirus infection completely. That's good news for individual health, but would still pose transmission risks. Tim O'Donnell