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Finding and testing all the contacts of every positive case is essential, experts said. At the peak of its epidemic, Wuhan had 18,000 people tracking down individuals who had come in contact with the infected.

At the moment, the health departments of some American counties lack the manpower to trace even syphilis or tuberculosis, let alone scores of casual contacts of someone infected with the coronavirus.

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When he lectured at a Singapore university, Dr. Heymann said, dozens of students were in the room. But just before he began class, they were photographed to record where everyone sat.

“That way, if someone turns up infected later, you can find out who sat near them,” Dr. Heymann said. “That’s really clever.”

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Also, experts emphasized, Americans should be taught to take seriously admonitions to stop shaking hands and hugging. The “W.H.O. elbow bump” may look funny, but it’s a legitimate technique for preventing infection.

“In Asia, where they went through SARS, people understand the danger,” Dr. Heymann said. “It’s instilled in the population that you’ve got to do the right thing.”

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Mr. Trump has said he could compel companies to prioritize making ventilators, masks and other needed goods. Some have volunteered; the Hanes underwear company, for example, will use its cotton to make masks for hospital workers.

He also has the military; the Navy is committing two hospital ships to the fight. And Mr. Trump can call up the National Guard. As of Saturday evening, more than 6,500 National Guard members already are assisting in the coronavirus response in 38 states, Puerto Rico and the District of Columbia.

High-level decisions like these must be made quickly, experts said.

“Many Western political leaders are behaving as though they are on a tightrope,” said Dr. David Nabarro, a W.H.O. special envoy on Covid-19 and a veteran of fights against SARS, Ebola and cholera.

“But there is no choice. We must do all in our power to fight this,” he added. “I sense that most people — and certainly those in business — get it. They would prefer to take the bitter medicine at once and contain outbreaks as they start rather than gamble with uncertainty.”

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The roughly 175,000 ventilators in all American hospitals and the national stockpile are expected to be far fewer than are needed to handle a surge of patients desperate for breath.

The machines pump air and oxygen into the lungs, but they normally cost $25,000 or more each, and neither individual hospitals nor the federal emergency stockpile has ever had enough on hand to handle the number of pneumonia patients that this pandemic is expected to produce.

New York, for example, has found about 6,000 ventilators for purchase around the world, Governor Cuomo said. He estimated the state would need about 30,000.

The manufacturers, including a dozen in the United States, say there is no easy way to ramp up production quickly. But it is possible other manufacturers, including aerospace and automobile companies, could be enlisted to do so.

Ventilators are basically air pumps with motors controlled by circuits that make them act like lungs: the pump pushes air into the patient, then stops so the weight of the chest can push the air back out.

Automobiles and airplanes contain many small pumps, like those for oil, water and air-conditioning fluid, that might be modified to act as basic, stripped-down ventilators. On Sunday, Mr. Trump tweeted that Ford and General Motors had been “given the go-ahead” to produce ventilators.

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Providers, meanwhile, are scrambling for alternatives.

Canadian nurses are disseminating a 2006 paper describing how one ventilator can be modified to treat four patients simultaneously. Inventors have proposed combining C-PAP machines, which many apnea sufferers own, and oxygen tanks to improvise a ventilator.

The United States must also work to increase its supply of piped and tanked oxygen, Dr. Aylward said.

One of the lessons of China, he noted, was that many Covid-19 patients who would normally have been intubated and on ventilators managed to survive with oxygen alone.