Mr. Duncan flew on Sept. 19 from Monrovia to Brussels, where, according to United Airlines, he took Flight 951 to Washington Dulles Airport and continued to Dallas/Fort Worth on Flight 822, arriving Sept. 20. Here in Dallas, the case was being handled with extraordinary caution and raised widespread concern.

Here in Dallas, there was no indication of panic among residents in the largely Hispanic and African neighborhood where Mr. Duncan was staying in the Fair Oaks section of the city. But misinformation about how the disease spreads was everywhere, even as local, state and federal health officials continued to make clear that Ebola is not an airborne illness and is not spread through casual contact but through direct contact with the bodily fluids of a sick person.

“We’re confident that it’s isolated and it’s being contained, but everyone is working tirelessly to double- and triple- and quadruple-check their work, to make sure that we’ve done an absolutely thorough job of identifying anyone who might be at any risk,” said the top elected official of Dallas County, County Judge Clay Jenkins.

Image Marie Wread, a friend of a neighbor of Marthalene Williams, became ill and was carried away by health workers in Monrovia on Wednesday. Credit... Daniel Berehulak for The New York Times

Some members of the Liberian community in the Dallas area said that given the spread of the disease in their home country, they were skeptical of the health information being released publicly, adding that public gatherings were being canceled out of fear of possible contagion.

At an African cafe down the street from the apartment complex where Mr. Duncan had been staying with relatives and a middle school attended by one or two of the students being monitored, a group of Ethiopian men and women sat talking at a table outside. No one knew Mr. Duncan or his family, and one woman was unfamiliar with Ebola and its effects.

“I touch you like this,” a man told her, tapping her on the knee, “and you get Ebola.”

Officials said Wednesday that they believed Mr. Duncan came into contact with 12 to 18 people when he was experiencing active symptoms and when the disease was contagious, and that the daily monitoring of those people had not yet shown them to be infected.