Updated at 3:38 p.m.

A top federal health official said Sunday that a man being treated for Ebola in a Dallas hospital is "fighting for his life," and he expressed confidence that the infection would not spread broadly to others through people with whom the patient has been in contact.

Thomas Frieden, the director of the Centers for Disease Control and Prevention, said Thomas Eric Duncan, who is in critical condition, remains the only person diagnosed with Ebola in the United States. Officials are closely monitoring people with whom Duncan has come into contact for signs of the infection, he said.

Authorities on Sunday also said they found a homeless man they described as a "low risk" individual who had gone missing and may have come into contact with Duncan. The man was taken a Dallas hospital for evaluation.

The CDC head made his remarks on CNN's "State of the Union" and in a briefing with reporters.

"We understand that his situation has a taken a turn for the worse," he said of Duncan. "We know that Ebola is a very serious disease, and we are hoping for his recovery."

He added, "There's no doubt that we can stop Ebola in this country."

Duncan remained in critical condition Sunday afternoon, the Texas Health Presbyterian Hospital in Dallas where he is being treated said. His condition worsened from serious to critical Saturday afternoon.

Frieden said experimental drugs were not being used to treat Duncan. He said such drugs "can be quite difficult for patients to take and may transiently worsen their condition."

Anthony Fauci, head of the head of the National Institute of Allergy and Infectious Diseases, said on CBS's "Face The Nation" that the experimental drug ZMapp "is difficult to produce" and that "a lot is being produced right now. It should be ready in a month and a half to two months."

Officials have been monitoring about 50 people who may have come into contact with Duncan to see whether they develop a fever. They will be monitored for 21 days, Frieden said.

Sana Syed, a spokeswoman for the city of Dallas, said Michael Lively, the homeless man who had gone missing, was found Sunday and was taken to Parkland hospital. Lively was seen Saturday and did not show any symptoms of Ebola, officials said. But they noted that like others, he must remain under observation.

"This is a low-contact individual that had been identified, that was seen yesterday and did not have any fever yesterday," said David Lakey, the commissioner of the Texas Department of State Health Services.

On ABC's "This Week With George Stephanopoulos," Frieden said there were no signs that any other people in the country had contracted Ebola.`

"We've had no other case," he said. "In fact, of the well over 100 cases we've been consulted about, the only one the staff told me, 'you know, we're really worried about this one,' was the patient in Dallas, even before his test results came back."

Also speaking on "This Week," Dallas Mayor Mike Rawlings said his city is "calm" but not taking the threat posed by Ebola lightly. Officials are vigilantly monitoring those who came into contact with Duncan, he added.

"We are playing man-to-man defense, if you will, in a compassionate way," said Rawlings.

Halfway across the country in Massachusetts, Richard Sacra, a doctor who was recently successfully treated for Ebola, was in stable condition in a hospital after he showed symptoms that appeared to be related to an upper respiratory tract infection, a physician treating him at a Worcester hospital said Sunday.

"Dr. Sacra remains in isolation until we can confirm with the CDC that he has no Ebola virus," said Robert Finberg, who is heading up Sacra's team of doctors. Doctors have sent blood work to the CDC to rule out Ebola, Finberg said.

Sacra contracted Ebola when he was working in Liberia. He was treated for the infection in Nebraska last month.

On ABC, Frieden said a recurring case of Ebola would be "extraordinarily unlikely."

"We've never seen that," Frieden said on "This Week." "But we're not going to take chances. So we'll test and — and we'll see. Time will tell."