“This won’t go away until we have an effective vaccine, hopefully in 12 months time,” said Walter Schachermayer, a professor of mathematics at the University of Vienna who was consulted by Mr. Kurz’s team on their exit timetable.

The idea that immunity would rise fast enough in any country to allow social distancing measures to be abandoned before then — without paying for it with an exorbitant death toll and overwhelming hospitals — was “a total illusion,” Professor Schachermayer said. “There is the constant risk of a second wave.”

After the Spanish flu first emerged in 1918, he noted, a second wave killed millions a year. There are already signs of a second wave now building in some East Asian countries that recently ramped up business.

That is why, even as Chancellor Kurz’s government announced its tentative opening, it made clear that the situation needed to be constantly monitored and reserved the right to impose restrictions quickly again.

“We will very closely monitor the number of new infections and will immediately pull the emergency brake if need be,” he said.

That monitoring will require a high volume of testing, Professor Schachermayer said. “It’s hard to get it right, because everything comes with a delay of two weeks” because of the virus’s incubation period, he said.

Even so, European leaders and their populations worry that the consequences of not allowing a broader resumption of economic activities could be devastating, too.