Connecticut and New Jersey have each reported at least one case.
On Sunday, officials said a Hartford County man in his 60s started developing mild symptoms on Nov. 27 after a family member tested positive. He was fully vaccinated.
Gov. Ned Lamont said the man's symptoms are mild.
"The good news is in the vaccination. In this case, the patient is at home resting peacefully, and no need to go to the hospital," he told CBS News' Margaret Brennan on Face the Nation.
Omicron has been found in at least a dozen states, and is spreading twice as fast as other variants in some places, officials said.
But for now, the Delta strain remains dominant, with new infections nationwide rising 36%. Hospitalizations are also increasing, with Rhode Island, Connecticut and Delaware among the hardest hit.
"The big question is whether or not Omicron will outcompete Delta. Remember, Delta is dominant, and that's an extremely dangerous variant," said Dr. Maria Van Kerkhove, a World Health Organization infectious disease epidemiologist.
"I'm concerned. Look, Omicron is coming up from New York on the I-95 corridor. But Delta is coming down from New Hampshire, Vermont, Massachusetts, and no state is an island, and no country is an island," Lamont added.
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Lamont urged residents in state to remain vigilant.
"The people of Connecticut have been through this for a year and a half. They're doing the right thing. Like I said, they're overwhelmingly getting vaccinated, they're more likely to wear a mask, do the right thing. So they don't need me pushing," Lamont said. "But there's no question about it. Especially folks of a certain age, stay out of contagious situations. We just don't know enough about this variant. Be careful."
Starting Monday, all inbound international passengers must now provide a negative COVID test to come into the U.S.
Nearly one-third of the country has yet to get a single vaccine dose, as officials brace for a winter surge. They urge people not to panic, and say if you are fully vaccinated, now is the time to get your booster.
Omicron has more than 50 mutations, including over 30 in the spike protein, making it easier to attach itself to human cells, officials told CBS2's Alice Gainer.
Virologist Alex Sigal heads the team at the Africa Health Research Institute.
"It's more of a Frankenstein than others. It's always something new. I mean, the virus keeps surprising us," Sigal said.
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Scientists are testing Omicron against the blood of fully vaccinated people and those previously infected, hoping to have results within the next week.
"The question right now is whether or not this is re-infecting people who have Delta immunity and haven't been vaccinated or whether it's going to also infect people who have been vaccinated. There's some reason to believe vaccines could be more protective than just immunity acquired through natural infection from Delta," said Dr. Scott Gottlieb, a former Food and Drug Administration commissioner.
At NYU Langone on Sunday, there was a call for more research and preparation. Sen. Kirsten Gillibrand and Rep. Carolyn Maloney joined doctors to push for passage of the "COVID-19 and Pandemic Response Centers of Excellence Act," which would provide federal funding to chosen academic medical centers.
"If we're going to have future epidemics and be responding to them, people need to be trained in that experience," said Dr. Jay Varma, a professor at Weill Cornell Medicine.
"They should be distributed to community health centers. They should be distributed by mobile vans," Schumer said.
CBS2's Alice Gainer contributed to this report, which first appeared on Dec. 5.
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