NEW YORK (AP) — Even as coronavirus deaths mount across Europe and New York, the U.S. and other countries are starting to contemplate an exit strategy and thinking about a staggered and carefully calibrated easing of the restrictions designed to curb the scourge.

“To end the confinement, we’re not going to go from black to white; we’re going to go from black to gray,” top French epidemiologist Jean-François Delfraissy said in a radio interview.

At the same time, politicians and health officials warn that the crisis is far from over despite signs of progress, and a catastrophic second wave could hit if countries let down their guard too soon. Deaths, hospitalizations and new infections are leveling off in places like Italy and Spain, and even New York has seen encouraging signs amid the gloom.

“We are flattening the curve because we are rigorous about social distancing,” New York Gov. Andrew Cuomo said. “But it’s not a time to be complacent. It’s not a time to do anything different than we’ve been doing.”

In a sharp reminder of the danger, New York state on Wednesday recorded its highest one-day increase in deaths, 779, for an overall death toll of almost 6,300.

“The bad news is actually terrible,” Cuomo lamented. Still, the governor said that hospitalizations are decreasing and that many of those now dying fell ill in the outbreak’s earlier stages.

In other developments:

— Stocks shot 3.4% higher on Wall Street amid the encouraging signs about the outbreak’s trajectory. The Dow Jones Industrial Average gained 780 points.

— U.S. researchers opened another safety test of an experimental COVID-19 vaccine, this one using a skin-deep shot instead of the usual deeper jab. A different vaccine candidate began safety testing in people last month in Seattle.

— British Prime Minister Boris Johnson spent a second night in intensive care but was improving and sitting up in bed, authorities said.

— Saudi Arabian officials announced that the Saudi-led coalition fighting Shiite rebels in Yemen will begin a cease-fire starting Thursday. They said the two-week truce was in response to U.N. calls to halt hostilities around the world amid the epidemic.

In China, the lockdown of Wuhan, the industrial city of 11 million where the global pandemic began, was lifted after 76 days, allowing people to come and go.

Wuhan residents will have to use a smartphone app showing that they are healthy and have not been in recent contact with anyone confirmed to have the virus. Schools remain closed, people are still checked for fever when they enter buildings and masks are strongly encouraged.

In the U.S., with over 14,000 deaths and 400,000 infections, the Centers for Disease Control and Prevention was considering changing self-isolation guidelines to make it easier for those exposed to someone with the virus to return to work if they have no symptoms.

Under the proposed guidance, aimed at workers in critical fields, such people would be allowed back on the job if they take their temperature twice a day and wear a mask, said a person who was familiar with the draft but was not authorized to discuss it and spoke on condition of anonymity.

Dr. Anthony Fauci, the nation’s top infectious-diseases expert, said that the Trump administration has been working on plans to eventually reopen the country amid “glimmers of hope” that social distancing is working to stop the virus’s spread.

“That doesn’t mean we’re going to do it right now,” he said on Fox News. “But it means we need to be prepared to ease into that. And there’s a lot of activity going on.”

The U.S. is seeing hot spots in such places as Washington, D.C., Louisiana, Chicago, Detroit, Colorado and Pennsylvania. The New York metropolitan area, which includes northern New Jersey, Long Island and lower Connecticut, accounts for about half of all virus deaths in the U.S.

In Europe, Italian Premier Giuseppe Conte is expected to announce in the coming days how long the country’s lockdown will remain in place amid expectations that some restrictions could be eased. Discussions are focused first on opening more of the country’s industries.