On Saturday, President Trump met with Judge Amy Coney Barrett, the nominee to the Supreme Court, and others in the Oval Office. On Tuesday, he debated former Vice President Joseph R. Biden Jr. in an indoor hall, neither with a mask, talking at high volume and often without pause.
On Wednesday, Mr. Trump traveled to and from Minnesota on Air Force One along with dozens of others. On Thursday, the president appeared indoors before hundreds of supporters at a golf club in Bedminster, N.J.
On none of these occasions was the president wearing a mask. Often, neither were many in the room or on the airplane with him. All in all, conditions like these are a recipe for so-called super-spreader events, in which a single infected person transmits the virus to dozens of others, research has shown.
“The White House has been flouting the basic rules of public health for a very long time,” said Dr. Ashish K. Jha, dean of the School of Public Health at Brown University in Providence, R.I. Regarding the president’s diagnosis that he was infected with the coronavirus, he added, “there are no surprises here.”
The problem is one scientists have been warning about for months: airborne transmission. In addition to the heavy droplets sneezed or coughed out by infected people, research has shown the coronavirus may drift in the air indoors, held aloft in tiny particles called aerosols.
Now the White House is trying to pin down exactly who had contact with Mr. Trump in recent days — and to whom these people in turn may have passed the virus. Potential contacts may number in the hundreds.
All of those people will have to be identified, tested and quarantined. “Rather than looking for a needle in a haystack, it’s like Trump is the needle and you’re trying to find out if it touched each piece of hay,” said Angela Rasmussen, a virologist at Columbia University in New York.
Experts may never know how the president was infected or whom he may have infected. The Rev. John I. Jenkins, president of the University of Notre Dame, tested positive for the coronavirus after attending a White House ceremony on Saturday for Judge Barrett. So did Senator Mike Lee, Republican of Utah.
The timing raises the possibility that the president could have been infected over the weekend, scientists said. Most people develop symptoms about five days after being infected with the virus, so exposure over the weekend would fit with reports that the president was showing early symptoms on Wednesday and Thursday.
People are thought to be most contagious to others a day or two before the onset of symptoms.
“We know that presymptomatic transmission drives a significant amount of spread of this virus,” Dr. Rasmussen said. “The bottom line is that you can be contagious before you know you’re sick.”
The presidential debate in particular resembles other indoor events at which widespread transmission has been documented — a gathering in a contained environment in which an infected person is speaking, coughing or even singing in proximity to others.
Mr. Biden tested negative for the virus on Friday. Still, given that Mr. Biden was only recently exposed, “He should quarantine and get tested again,” Dr. Rasmussen said. (Mr. Biden said he would go ahead with a campaign event in Michigan planned for Friday.)
Others in the debate auditorium, too, may have been at risk.
Aerosols are expelled when people talk, shout, sing or breathe. The longer an infected person is in an indoor space, the greater the risk. Mr. Trump was in the debate hall for at least the 90-minute duration.
“He was doing a lot of talking, a lot of shouting,” said Linsey Marr, an expert in airborne transmission of diseases at Virginia Tech in Blacksburg, Va.
The president and Mr. Biden were at lecterns more than six feet apart at the debate. At that distance, Mr. Biden might have had protection from larger respiratory droplets released by the president, but not from aerosols lingering in the air.
Indoors, aerosols may travel farther than six feet. In August, for example, scientists reported that they had successfully isolated live virus from aerosols collected at a distance of seven feet and 16 feet from an infected patient in a hospital.
Dr. Marr likened the aerosols released while talking or shouting to cigarette smoke. People closest to the smoker — like Mr. Biden and the moderator, Chris Wallace (who plans to take a test on Monday) — would have been exposed first.
But over time, the smoke in a poorly ventilated room will drift throughout the space and reach even those much farther away.
Anyone with a face covering would be at least partly protected from the virus. But most of Mr. Trump’s family members and associates did not wear a mask during the debate, despite requests by the venue hosts, the Cleveland Clinic, to do so.
“Now the question becomes, what is the ventilation?” Dr. Marr said.
Representatives of the Cleveland Clinic did not immediately respond to requests for information about ventilation in the debate room, placement of the lecterns and other details that may bear on whether the president may have infected others.
In a prepared statement, Halle Bishop Weston, a spokeswoman for the Cleveland Clinic, said Mr. Trump, Mr. Biden and people traveling with them had been tested for the virus by their campaigns, and were said to be negative. Everyone gaining entry to the debate hall had tested negative for the virus, she added.
Safety measures at the debate aligned with guidelines from the Centers for Disease Control and Prevention and included “social distancing, hand sanitizing, temperature checks and masking,” the statement said.
The debate was held in a large space with high ceilings, “so there is a lot of air into which infectious aerosol could be dispersed and diluted,” said William Bahnfleth, an architectural engineering expert at Penn State University in University Park, Pa.
“I’d imagine that the greatest risk at this event was due to some of the participants not masking and distancing,” he added. “The first lady would have been in the location most likely to pose risk to others in the audience.” (Mrs. Trump also tested positive for the coronavirus, according to an announcement early Friday.)
Several members of the Trump family did not wear masks during much of the debate. And experts noted that inadequate ventilation could have fostered spread of the virus.
“This is something that needs to be looked at in every indoor environment, be it schools, offices or certainly in a high-profile event like this,” said Joseph Allen, an expert on building safety at the Harvard T.H. Chan School of Public Health.
Ventilation becomes especially important when many people are gathered with an infected person for a long period.
“That’s exactly what we had at the debate,” Dr. Allen said. “The president was speaking often and loudly, for the full hour and a half.”
In addition to the debate, the president is likely to have spent time with his inner circle in other rooms, Dr. Allen added.
The C.D.C. has not fully acknowledged the risk of airborne transmission of the virus indoors, beyond indirect nods to the importance of ventilation in schools and businesses.
On Sept. 18, the C.D.C. published a new version of its guidance on how the virus spreads that acknowledged the importance of aerosols, and said inhalation of the virus was the main way the virus was transmitted.
Before that, the agency had emphasized hand hygiene, wearing face coverings and maintaining six feet of distance as the primary ways for people to protect themselves.
The version posted Sept. 18 also said that indoors, “there is growing evidence that droplets and airborne particles can remain suspended in the air and be breathed in by others, and travel distances beyond 6 feet (for example, during choir practice, in restaurants, or in fitness classes).”
But that guidance was removed from the agency’s site three days later and replaced with a document that no longer mentioned aerosols or airborne transmission. At the time, C.D.C. officials said the revised document had been posted in error and had not yet been cleared by rigorous scientific review.
But given the many recent reports of meddling by the White House and the administration in C.D.C. science, some public health experts feared that the agency had been ordered to take down the acknowledgment of aerosols and airborne transmission of the coronavirus.