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Top U.S. health officials are urging caution amid reports of coronavirus cases peaking in some areas and speculation that the omicron variant could end the pandemic.

“It is an open question whether it will be the live virus vaccination that everyone is hoping for,” Anthony Fauci, the president’s chief medical adviser, said Monday during a virtual panel at the Davos economic forum.

“I would hope that that’s the case. But that would only be the case if we don’t get another variant that eludes the immune response of the prior variant,” he said. Even then, he added, covid-19 probably would remain as an endemic disease worldwide.

“If you look at the history of infectious diseases, we’ve only eradicated one,” he said. “And that’s smallpox. That’s not going to happen with” the coronavirus.

Surgeon General Vivek H. Murthy expressed a similar note of caution Sunday on CNN, saying that despite apparent omicron peaks in pockets of the Northeast, much of the country isn’t there yet. “The next few weeks will be tough,” he said.

Meanwhile, Pfizer chief executive Albert Bourla predicted that “we will soon be able to resume a normal life” given pandemic mitigation measures including tests and vaccines. But he also said that doesn’t mean an end to the coronavirus.

“We’ve had so many surprises since the start of the pandemic,” he said in an interview with the French newspaper Le Figaro, published Sunday. “We will probably have to live for years with a virus that’s very difficult to eradicate.”