Airlines are slashing flights and freezing hiring as they experience a sharp drop in bookings and a rise in cancellations in the face of the spreading coronavirus.

Southwest Airlines CEO Gary Kelly says the outbreak might be worse for airlines than the terror attacks of 2001. An industry trade group believes it will be more damaging.

Delta Air Lines said today that travel demand has fallen so badly in the past week that it expects one-third of seats to be empty this month on flights within the United States, which was insulated from virus fallout for a time.

United Airlines expects to lose money in the first quarter for the first time in six years.

Business travelers are grounded as meetings and conferences are canceled. Leisure travelers are scared.

Normally airlines try to lure reluctant travelers by cutting fares, but that won’t work with the COVID-19 outbreak.

“If you are scared of flying, you are probably scared at any price,” said Delta President Glen Hauenstein.

Delta, the world’s biggest airline by revenue, said net bookings declined 25% to 30% in the past two weeks and could get worse. It will cut international flights by 20% to 25% and reduce U.S. flying by 10% to 15%, roughly matching cuts previously announced by United Airlines.

Delta is also cutting spending, putting a freeze on hiring, offering voluntary unpaid leave, delaying voluntary pension contributions and suspending share buybacks.

American Airlines announced it will cut international flying by 10% this summer and reduce U.S. flying by 7.5% in April. It has delayed training of new pilots and flight attendants.

United arranged $2 billion in additional bank credit to raise liquidity from $6 billion to $8 billion. President Scott Kirby said United hopes the outbreak won’t be as damaging as 9/11, when bookings plunged 40% for two months before starting to recover, “but we’re not willing to count on that.”

Kirby and United CEO Oscar Munoz will waive their base salaries through June, and Kelly, the Southwest CEO, said he will take a 10% pay cut.

In a video to employees, Kelly said the virus poses a problem not seen since the 9/11 attacks, “and it may be worse.”

Airline stocks have been among the hardest hit during the current market slump, but they soared today. American, which lost half its value since mid-February, jumped 13% and United was up nearly 12% in afternoon trading. Delta and Southwest, which had fallen less, were up about 2%.

The International Air Transport Association, an airline trade group, estimates that the outbreak could reduce carriers’ revenue by between $63 billion and $113 billion depending on how far and deep it spreads. The same group said the terror attacks in 2001, which devastated the U.S. airline industry but had less impact overseas, cut revenue by about $20 billion.

European airports expect 187 million fewer passengers this year because of the outbreak. Airports in Italy, where a nationwide quarantine was put in place Tuesday, are most affected. Airport officials urged the Italian government to provide emergency financial support, and said aid might be necessary in more countries if authorities clamp down on travel.

Discount carrier Norwegian Air said today it would cut 15% of its flights through mid-June and lay off a “significant share” of its workers. It called the unspecified number of job cuts temporary. Air France-KLM said it has canceled 3,600 flights this month.

Those moves come on top of announcements that Germany’s Lufthansa will cut up to half its flights after a “drastic” drop in bookings, and Finland’s national carrier, Finnair, will furlough workers for up to a month and cancel 1,400 flights.

The demand drop-off that began in Asia picked up steam in the U.S. about two weeks ago, when the virus spread outside Asia, notably to Italy. It has been felt equally among business and leisure travelers.

Delta’s Hauenstein said demand has fallen more sharply on the West Coast — Washington state and California have suffered larger outbreaks — than on the East Coast. He said younger people have been more willing to keep flying; people over 55 less willing.

The virus appears to be most dangerous among older people. The Associated Press reported over the weekend that the White House overruled a plan by the Centers for Disease Control and Prevention to recommend that older and physically weak Americans be advised not to fly on commercial airlines because of the new virus, according to a federal official. Instead, the CDC issued more nuanced advice, saying older people and those with health problems should avoid cruise ships, crowded places and “non-essential travel such as long plane trips.”

American Airlines CEO Doug Parker said the largest decline has been in tickets within seven days of departure, which he said was entirely due to corporations restricting travel by employees. He predicted that business travel will return, but he didn’t say when.

Airlines have been waiving change fees and touting stepped-up cleaning of airplane cabins to make passengers feel more comfortable about flying.

They have also cut prices, although that has not stemmed the drop in demand. Hopper, a travel-data research firm, said the average domestic airfare fell 14% last week, with fare-sale discounts running more than 50% on some major routes such as New York-Chicago and Los Angeles-Washington.

Delta, United, American and most international carriers have suspended flights to China and reduced flights elsewhere in Asia.

U.S. airline officials say they can manage their way through the outbreak. They say their companies are stronger, more profitable and carrying less debt than in the past. Mergers have left fewer competitors. Lower oil prices will help — American expects to spend $3 billion less on fuel.

The airlines, however, are facing a challenge unlike any they have seen before.

“This current crisis is a test of the ability of our restructured industry to withstand the types of shock that we have never been able to withstand before,” American’s Parker said.