DALLAS — On any other day, the United Parcel Service worker who delivers to the Ivy Apartments here would have made his rounds and handled his packages with his bare hands. But these are not ordinary times in this working-class immigrant community northeast of downtown.

On Friday afternoon, the deliveryman, parked across the street from the apartment complex, wore black athletic gloves, fearful of Ebola. The Ivy is where the man with the first case of Ebola diagnosed in the United States had been staying since arriving from Liberia, and where four people close to him have been quarantined by health officials.

“I started wearing them as soon as I found out what happened over there,” the U.P.S. deliveryman, who asked that his name not be used because he was not authorized to talk to the news media, said of his gloves. “I’m terrified, to be honest with you. People have to sign. I’m really scared for them to even touch my board.”

The Ebola crisis that has been unfolding in Dallas has had a subtle, but distinct impact on daily life near the apartment where the Liberian man whom city officials call Patient Zero was living — the limiting, however unnecessary, of “direct contact” among strangers, neighbors, friends and classmates. People have gone about their daily affairs without widespread panic, but they have done so washing their hands more often than they typically would, using hand sanitizer at the mere mention of Ebola and being wary of casual contact that would not have merited a second thought in the past.

Some of the parents at the schools that several students who came into contact with the patient attended have been telling their children not to shake classmates’ hands, or they have kept their children at home. One high school senior said he thought about wearing a medical mask to school but could not find one.

Stanley Gaye, president of the Liberian Community Association of Dallas-Fort Worth, said when he encounters people who have recently been to Liberia, he asks how long they have been back. He declines to shake their hands if they have been back fewer than 21 days, the typical incubation period for the virus.

Nathan S. Kortu, the bishop of New Life Fellowship Church in nearby Euless, which hosted an emergency meeting of the Liberian community, planned to tell his congregation on Sunday that anyone hosting recent arrivals from Liberia at their homes should make them sleep in a separate bedroom for 21 days.

Maru Mekonen, 49, an Ethiopian who owns Maru Computer Services, a repair shop near the Ivy, used to shake hands with his customers when they stepped inside, particularly his Ethiopian customers.

“No more,” Mr. Mekonen said. “When my customers come, I used to just shake first and say, ‘How are you?’ Now I just say, ‘Hey,’ and stop.”