An ambulance driver wearing a protective suit escorts Amber Joy Vinson (not shown), the second health worker to be infected with the Ebola virus at Texas Health Presbyterian Hospital to the airport in Dallas, Texas, Oct. 15, 2014. Reuters

President Barack Obama and other national leaders have reassured Americans that the Ebola virus is under control and won't spread, but travelers seem unconvinced. Airline stocks sank amid reports Wednesday that 26-year-old Ebola patient Amber Vinson flew on a commercial plane from Ohio to Texas this week with a slightly elevated temperature.

The panic appears largely overblown. Health officials said it's highly unlikely that Ebola can spread simply by sitting next to someone with a fever on a plane. Airplanes are lightly cleaned between flights and undergo heavier cleaning on down time. The sweeps help prevent transmission of common diseases, like the flu.

It's unlikely the virus would spread on an airplane unless a passenger were to come into contact with a sick person's bodily fluids, Dr. Marty Cetron, director of the Centers for Disease Control and Prevention's Division of Global Migration and Quarantine, said. "This is not an airborne transmission," Cetron told CNN. "There needs to be direct contact frequently with body fluids or blood."

Vinson wasn't showing symptoms when she flew but had a slightly elevated temperature of 99.5. There have been no confirmed cases of Ebola becoming airborne despite multiple outbreaks in Africa since 1976.

“The fact that the patient number two did not have a fever until the next day, did not have nausea or vomiting on the plane, suggests to us that the risk to anyone around that individual on the plane would have been extremely low,” Thomas Frieden, director of the CDC in Atlanta, said. "If you are a member of the traveling public and you are healthy, should you be worried that you might have gotten it by sitting next to someone, and the answer is no."

Still, public health officials said Wednesday they were tracking down 132 people who were on the flight with Vinson from Cleveland to Dallas. Ebola symptoms include fever, muscle pain, vomiting, diarrhea and internal and external bleeding, according to the World Health Organization.

The Ebola panic comes ahead of the busy holiday travel season, a time when passengers often have runny noses and high fevers from the flu or a cold. "Passengers can best protect themselves by just doing the routine, common thing: bring some alcohol-based sanitizer," Barbara Peterson, senior aviation correspondent for Condé Nast Traveler, said. "But with the flu-season coming up, keep it in perspective. There is no serious threat of catching something simply because you're in an airplane cabin."

Airline stock prices have taken a hit in recent weeks. Delta Air Lines and United Airlines shares fell more than 1 percent Wednesday. A New York Stock Exchange index of airline stock is down 11.57 percent over the last month.

Some passengers have begun to take extra precautions. Travel blogger Johnny "Jet" DiScala visits 20 countries and flies about 150,000 miles annually. To avoid panicking over Ebola, he told CNN that he carries surgical masks, which he will wear and offer to travelers "coughing and sneezing on me."