DALLAS — There is Ebola, and then there is fear of Ebola.

For the thousands of parents and schoolchildren in the Dallas-Fort Worth area, it is a concern that they wrestled with on Thursday morning after learning that five school-age children had had contact with a man who is ill with the disease.

“My mom, she recommended that I not touch a lot of kids at school,” said Royale Hollis, 15, a freshman at Emmett J. Conrad High School, which at least one of the children attended. “I haven’t been shaking hands, just bumping elbows. People just keep their distance. Girls don’t give boys hugs. We’re all cool with each other but we just don’t want to catch anything.”

The school is just around the corner from an apartment complex where the Ebola patient, Thomas E. Duncan, was staying before he was rushed to the hospital and given the diagnosis.

Mr. Duncan, who is in isolation at a Dallas hospital, came into contact with five children who went to four different schools — a high school, a middle school and two elementary schools.