DALLAS — News that a nurse diagnosed with Ebola flew on a plane full of passengers raised fear among airline investors that the scare over the virus could cause travelers to avoid flying.

Shares of the biggest U.S. airlines tumbled between 5 and 8 percent before recovering in afternoon trading. The overall market slumped on concern about slowing global economic growth, but recouped some losses late in the day.

Health officials downplayed the possibility that any of the 132 passengers on Frontier Airlines Flight 1143 from Cleveland to Dallas-Fort Worth could have been infected, because the nurse showed no Ebola symptoms during the flight. Nonetheless, public health officials were notifying other passengers.

Hoping to minimize the impact of Ebola, the airline industry is banking on assurances from health experts that the virus is spread only through contact with the bodily fluids of someone already showing symptoms, and the presumption that someone that sick would not be physically able to travel.

Tony Tyler, CEO of the International Air Transport Association trade group, said Ebola was unlikely to reduce travel.

“You can’t rule out that worry about this disease could cause a drop in traffic,” he told reporters in San Diego. “My personal view is that is unlikely.”

Robert Mann, an aviation consultant and former American Airlines executive, said the decision to notify other passengers on the flight was made out of extra caution, “but all that rational thought aside, it may cause some people to delay trips.”

Dr. Tom Frieden, the director of the U.S. Centers for Disease Control and Prevention said it was extremely unlikely that passengers could have contracted the disease because the nurse, Amber Joy Vinson, was not vomiting or bleeding. But, he said, she should not have been on the flight because of the possibility that she had been exposed to Ebola and because she had a slightly elevated fever.

The CDC later confirmed that an official responsible for monitoring Vinson cleared her to fly. Frieden said that from now on, no one involved in caring for the original Ebola patient in Dallas would be allowed to travel except “in a controlled environment.” CDC guidelines say people possibly exposed to Ebola should avoid commercial flights for 21 days.

Frontier said Flight 1143 was that particular plane’s last flight on Monday night, and it was cleaned overnight according to CDC standards before being used Tuesday. On Wednesday night, the plane was flown without passengers to Denver, where Frontier said it would be cleaned for a fourth time.