President Donald Trump, who is hospitalized with the coronavirus at Walter Reed Medical Center, is now being given a second experimental drug for treatment, as more members of his inner circle like Kellyanne Conway and Chris Christie and other leaders test positive for COVID-19.

His physician said at a news conference on Saturday that Trump was "doing very well" and that he and the medical team were "extremely happy at the progress" they have seen.

The president is staying at the Walter Reed Medical Center for a few days "out of an abundance of caution," and his physician, Dr. Sean Conley, said in a late Friday night press release that he now taking remdesivir.

Remdesivir, a drug developed by Gilead, was originally intended to treat the Ebola virus but was never approved for that usage. However, this spring, the Food and Drug Administration approved it as an emergency treatment for COVID-19 after trials showed positive signs for some patients. Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, said, "This drug happens to be blocking an enzyme that the virus uses."

"Going well, I think! Thank you to all. LOVE!!!" Trump tweeted at 11:31 p.m. on Friday, almost 23 hours after first revealing he was sick. He had also released a video of him discussing why he was going to Walter Reed, just as he was walking to Marine One to be transported there, saying, "I think I'm doing very well":

In the days since Trump announced that he and First Lady Melania Trump have the coronavirus, numerous people have been diagnosed with the virus. In addition to top aide Hope Hicks, whose positive result was known on Wednesday (and Trump, on Thursday, still traveled to a fundraiser in Bedminster, N.J. where mask-wearing was largely absent), others who now have the virus include Trump campaign manager Bill Stepien; former senior advisor Conway; former NJ governor Christie, who helped the president prep for the debate; Republican National Committee chairwoman Ronna McDaniel; Republican Senators Ron Johnson, Mike Lee, and Thom Tillis; and the president of Notre Dame, John Jenkins.

Many of these people, including Lee, Conway, and Jenkins, in addition to the Trumps, were at the Rose Garden press conference to announce the nomination of Amy Coney Barrett to the Supreme Court.

The Rose Garden event is remarkable in that amidst a global pandemic, which has afflicted over 7 million Americans, killing nearly 210,000, hundreds of people were gathered without social distancing and many without masks. Trump, though, has repeatedly insisted to the public that the pandemic is "rounding the corner." This week, 24 states are reporting more COVID-19 cases than last week, as public health experts say that a second wave is not a matter of if but when.

President Donald Trump, center, stands with Judge Amy Coney Barrett as they arrive for a news conference to announce Barrett as his nominee to the Supreme Court, in the Rose Garden at the White House in Washington, D.C., on September 26, 2020

There was also an indoor White House event for Barrett's nomination:

Almost a dozen people—including organizers and members of the media—of Tuesday's presidential debate in Cleveland have the virus, as do three journalists in the White House press corps. The White House Correspondents Association has previously criticized the White House's safety measures during press briefings.

Public health experts believe that the coronavirus is transmitted by respiratory droplets, and they all agree that mask-wearing and social distancing are key to mitigating the spread of the disease. While the White House has a regular testing protocol, masks and social distancing do not appear to have been consistently implemented. The Wall Street Journal reports, "The president has maintained that he doesn’t need to wear a mask because he and the people in close proximity to him are tested for the virus. But only staffers who interact with the president are tested regularly, leaving the hundreds of others who work in the White House complex vulnerable."

Ashish Jha, the dean of the Brown University School of Public Health, told StatNews, "For someone as important as the president, you always need a layered protection. People around him should be wearing masks. I think testing is great, and I’ve obviously been a huge advocate of it. But we should really limit the number of contacts he has, and limit the number of contacts that people who contact [Trump] have."

At a Saturday morning press conference at Walter Reed, the president's medical team spoke about his condition in positive terms. Dr. Sean Dooley said that the president will be on a five-day course of remdesivir, adding that Trump was in good spirits and felt like he could "walk out of here today":

They also indicated that Melania Trump, who is at the White House, is doing well. They explained that Trump was at Walter Reed "because he's the president of the United States," noting that they want to give him the best medical care. His team is monitoring his heart, liver, and kidney functions, and said his oxygen saturation level is 96%, which is high.

The physicians emphasized that the president was not receiving oxygen "today," and Conley said, after repeated questioning, "Thursday no oxygen. None at this moment and yesterday with the team, while we were all here, he was not on oxygen.” The president arrived at Walter Reed after 6:30 p.m.

They also declined to discuss Trump's past COVID-19 tests, leaving questions about whether his campaign should have gone ahead with the N.J. fundraiser to meet with donors despite knowing about Hicks' positive diagnosis and whether he was tested before the event. The Centers for Disease Control and Prevention says that people should quarantine after steady contact with someone who has the coronavirus.

Conley characterized Trump's case as being "72 hours into the diagnosis." He did not indicate when the president would be released.

A source told the White House pool covering the Walter Reed presser, "The President's vitals over last 24 hours were very concerning and the next 48 hours will be critical in terms of his care. We are still not on a clear path to a full recovery."