The U.S. Centers for Disease Control said Wednesday that Texas nurse Amber Vinson had traveled on a Frontier Airlines flight from Cleveland to Dallas a day before being diagnosed with Ebola.
On CNBC's "Halftime Report," Gordon Bethune, who helmed Continental from 1994 to 2004, said that airlines were counting on federal officials to maintain public confidence.
"They are going to rely on the government and the CDC to protect them," he said.
Bethune added that he didn't think airlines had seen a large drop in bookings, nor were they likely to curtail flights yet.
"I don't think they would do that without some consideration with the government," he said. "I do know, though, that things like sick calls from crews that won't want to go will increase, so there will be some delays and cancellations if this thing gets out of control. But we're a way from that happening."
Bethune said that airlines were likely to work on maintaining the public's trust.
"I think much like (Frontier Airlines CEO David Siegel), you cooperate with the government, clean the airplane to establish there's no continuing threat, but after that it's an ex post facto world," he said. "There's nothing you can take back, and that is out of your hands as an airline. You're just a transportation provider."
Bethune added that the one bit of good news for the airlines to offset Ebola fears was the decline of crude oil prices to around $80 per barrel.
"Well, they're high-fiving it. They were taking the lumps back when it was at $50 and went to $80. Now that $80 looks good, they've shown a lot of discipline in pricing, and I think this'll be a good upside for them," he said. "I'm really happy for the industry."