Paul J. Richards | AFP | Getty Images  Twilette Miller, a nurse arrives from Dayton, Ohio, at Dulles International Airport Oct. 16, 2014, outside Washington, D.C.  Fawley is one of many travelers worried the Centers for Disease Control and Prevention (CDC) doesn't fully understand the threat of the Ebola virus. His comments came earlier Thursday, before the White House said it is still against putting in place a travel ban on West African countries.  Read MoreEbola impact on airlines limited for now  Meanwhile, the CDC is reaching out to 132 people who were on Frontier Airlines Flight 1143 with Amber Vinson, the second Ebola-stricken Texas nurse. Vinson arrived in Ohio on Friday Oct. 10 and returned to Dallas Monday night. On Tuesday, she was diagnosed with a fever and later tested positive for Ebola.  Frontier Airlines has since taken the Airbus A320 out of service. The plane was ferried back to Frontier's base in Denver, where it was cleaned. The airline also replaced air filters and some of the seat covers and carpeting on the plane.  Frontier CEO David Siegel said, "These extraordinary actions went beyond CDC recommendations. These steps were taken out of concern for the safety of our customers and employees."  Most passengers we spoke to had no complaints about Frontier or how it responded to the Ebola crisis.  Read MoreCompany sells out of Ebola-inspired plush toy  They did not have as much confidence in the CDC.  "The CDC is mishandling this," Greg Powell said. "They didn't have a grip on this from the start, they had a slow handle on this, so that is what I am concerned about. How many more people are out there that have been exposed?"  It's that fear of the unknown that worries people like Esther Viets. She was waiting at the Dallas Ft. Worth Airport to pick up a relative.  "I don't feel safe to fly. I'm not going to fly. Like I said, I don't even feel comfortable being the airport right now," she said.  Passenger Brittany Wilson sounded a similar note. As she checked bags for a flight from Dallas to Atlanta, she wore a surgical mask around her neck. It was another layer of protection she planned to wear during her flight.  "You can't be too cautious, so I would just rather protect myself as well as I can, so I just decided to wear it," she said. "I just feel as though it is something that they are not telling us."  The CDC has been working to assure the public that a widespread outbreak of Ebola is unlikely. On Thursday, the agency's Dr. Thomas Frieden said, "There is zero doubt in my mind unless there's a mutation there will not be a large-scale outbreak in the U.S."  Despite travelers' nerves, United Continental, JetBlue and Delta shares were all trading higher.
"I am not losing anything by putting on gloves and a mask. It is just an extra precaution," one man said.