DALLAS — Health officials in Texas said Thursday that they had reached out to as many as 100 people who may have had contact — either directly or indirectly — with a Liberian man sick with the Ebola virus while he was contagious.

Of those people, only a handful have been isolated, including family members and the medical technicians who rushed the patient, Thomas E. Duncan, to the hospital on Sunday. Most on the list are there simply because they had contact with people who had had contact with Mr. Duncan.

A spokeswoman for the Dallas County health and human services department, Erikka Neroes, said the initial list of 12 to 18 people thought to have direct contact with Mr. Duncan had been expanded to people who had either direct or secondary contact.

“None are symptomatic,” Ms. Neroes said.

“It’s a constant process of interviews and locating as many contacts as are out there,” she said. “We expect daily that there could be more people added.” Others could fall off the list as time passes and they show no symptoms. “It’s constantly evolving,” she said.

Even as health officials scrambled to find and monitor those people, a group that includes five school-age children, they sought to ease concerns among Dallas residents.

The Texas health commissioner, Dr. David Lakey, said Thursday that four members of Mr. Duncan’s family had been told to remain home and not to have visitors.

“We have tried-and-true protocols to protect the public and stop the spread of this disease,” Dr. Lakey said. “This order gives us the ability to monitor the situation in the most meticulous way.”

The five children who came in contact with Mr. Duncan were being kept home from school, and local officials tried to reassure parents at the four different schools they attended that the facilities were thoroughly cleaned and that children are safe. There were reports that some parents were keeping their children home.

At the same time, there were more questions about how the case was handled by local doctors and health officials as the timeline on Mr. Duncan’s activities shifted.

Initially, federal authorities announced at a news conference on Tuesday that Mr. Duncan first sought treatment at the hospital last Friday, Sept. 26, but that account has since been changed. The hospital issued a statement saying that the patient went there after 10 p.m. Sept. 25, when he was examined and sent home. Neither the hospital nor the federal Centers for Disease Control and Prevention explained how officials had gotten the date wrong and what effect it may have had on the investigation.

The woman who was hosting Mr. Duncan in Dallas told CNN on Thursday that she had brought him to the hospital the first time and twice told hospital workers he had been in Liberia. Still they sent him back with only some antibiotics to the apartment, where the woman was staying with one of her children and two nephews.

Over the next two days, Mr. Duncan began sweating profusely and had diarrhea. The sweaty sheets were still on her bed, she said. She put the towels he used in a bag but did not know what to do with them.

The woman, whom CNN did not identify by name, said she had no symptoms at this point.

On Thursday, Mr. Duncan’s nephew said that even after his uncle was rushed to the hospital three days after his initial visit, vomiting and gravely ill, he did not feel they were acting with enough urgency and called federal authorities himself to alert them to the situation.

“I called C.D.C. to get some actions taken because I was concerned for his life and he was not getting the appropriate care,” the nephew, Josephus Weeks, told the NBC program “Today.” “And I feared that other people might get infected if he was not taken care of.”

Dr. Anthony S. Fauci, the head of the National Institutes of Health, acknowledged that things could have been handled better, but said he was confident the measures being taken would prevent any outbreak of the disease.

“It is regrettable that there wasn’t the connecting of the dots,” Dr. Fauci told CNN on Thursday. “Because of the attention that has been paid to the situation in Dallas, people will be very much aware of paying attention to the travel history.”

The immediate priority of health officials is contacting all those who might have come into contact with Mr. Duncan after he became symptomatic, which is when the disease can spread.

Health officials said to think of the contact tracing as moving in concentric circles. Health officials focused first on those who had the closest and most intimate contact with Mr. Duncan after he became symptomatic because they are at the greatest risk of infection. That group includes at least four family members and three medics who are being isolated.

The next group includes those who had more casual contact with Mr. Duncan after he grew sick. More than a dozen people in this category will monitored by the authorities for 21 days, which is the longest documented time it has taken for this strain of Ebola to begin to cause illness.

These people will have their temperatures checked daily but are free to go about their daily routines unless they begin to show symptoms.

The final group includes the secondary contacts — those who came into contact with people who came into contact with Mr. Duncan. Since the risk of infection in this group is minimal, they are not monitored daily. But their names are put in a database in case any one of them unexpectedly becomes ill and so authorities know how to reach them quickly if needed.

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Dr. David Lakey, Texas health commissioner, held a news conference in Dallas on Wednesday. Credit Mike Stone/Reuters

“The people who were in the emergency response as well as the family, who had very close contact, even with bodily fluids, they are at a higher risk than others who came in contact,” Dr. Fauci said. “As you monitor them for fever and symptoms, you want them in a place that is confined.”

Mr. Duncan remained in isolation at Texas Health Presbyterian Hospital on Thursday, in stable but serious condition. Mr. Duncan probably became infected in Monrovia, the Liberian capital, on Sept 15, when he helped carry his landlord’s convulsing pregnant daughter to a clinic to be treated for Ebola.

The woman, 19-year-old Marthalene Williams, was turned away from the overcrowded clinic because it did not have room for her and died the next day. The landlord’s son and three neighbors who came in contact with the woman also died soon afterward.

Mr. Duncan went to the airport in Monrovia on Sept. 19 to board a flight to Brussels and then on to the United States. From Brussels, Mr. Duncan flew to Dulles International Airport, near Washington, on Sept. 20 on United Flight 951, and then on to Dallas-Fort Worth on Flight 822, the airline confirmed.

Four days later, on Sept. 24, Mr. Duncan told doctors, he started to get sick. On Sept. 25, he went the emergency room with a fever and nausea.

He was sent home under the mistaken belief that he had only a mild fever, a hospital administrator said; the information that he had traveled from Liberia, one of the nations at the heart of the Ebola epidemic, was overlooked.

He returned to the hospital on Sept. 28, this time sped there in an ambulance and gravely ill.

Containing the spread of Ebola in Dallas now depends on the effectiveness of contact tracing, the federal disease centers’ core strategy. Having patient zero — the first one infected — in hand is a rare luxury in the word of contract tracing and should help ensure that the authorities cast a wide enough net to find anyone at risk.

Ten C.D.C. members are in Texas assisting local officials. They include three senior scientists with expertise in public health investigations and infection control, a communications officer, five Epidemic Intelligence Service officers — the centers’ disease detectives — and a public health adviser

“Every health department has an unsung hero who tracks down people,” said Jennifer Nuzzo, an epidemiologist with the UPMC Center for Health Security in Baltimore. “They are generally really low paid jobs, but people tend to stay at them for a long time. It’s a labor of love.”