Further evidence of the impact of social distancing is found in California, where many counties moved early to impose stay-at-home orders and where researchers have reduced their death toll projections. The state is now loaning hundreds of ventilators to other places in need.

Gov. Gavin Newsom on Tuesday even referred to a “sense of optimism” that the state had kept its rate of infections below the levels that would strain hospitals.

Tempering that optimism are the sheer numbers in California — 17,000 coronavirus cases and at least 440 deaths — as well as the prediction by state officials that waves of infection will continue. Dr. Mark Ghaly, the secretary of the California Health and Human Services Agency, said the state’s peak would come in late May.

With so many uncertainties about the course of the coronavirus at play — in good measure because so little actual testing has been conducted — city and state leaders have seized on the apparent effects of social distancing as a way to raise hopes and rally their communities to stay the course.

In Detroit, which has reported more than 5,800 cases and more than 250 deaths, hospitals cannot handle the number of sick and a convention center has been converted into a field hospital. Hundreds of public employees have been quarantined and thousands of health care workers have tested positive for the virus. Fear pulsates through the empty streets of the city.

But Mayor Mike Duggan on Tuesday reported what he called “the first glimmer of light” — indications that social distancing was slowing the city’s death rate.

He seemed to channel Winston Churchill in both his candor and reassurance.

“We’re going to lose a lot of our neighbors in the coming days,” Detroit’s mayor said. “It’s going to get worse before it gets better. But we can beat this if we keep doing what we’re doing.”

Reporting was contributed by Mike Baker, John Eligon, Thomas Fuller, James Glanz, Joseph Goldstein, Jason Horowitz, Danielle Ivory, Sarah Kliff, Amy Qin, Mitch Smith and Karen Yourish.