DALLAS (AP) — United Airlines warned Thursday that bookings have slowed and cancellations have increased as the number of coronavirus infections spikes across the country.

Southwest Airlines has also seen more cancellations, and the carrier's CEO said that travel demand will be remain weak in the first quarter.

The number of people flying in the United States is down about 65% from a year ago, and airlines were hoping that the upcoming holidays would mean an increase in leisure travel.

United said however that it continues to see the virus hurting travel.

In the past week, “there has been a deceleration in system bookings and an uptick in cancellations as a result of the recent spike in COVID-19 cases,” United said in a regulatory filing.

Chicago-based United expects to operate no more than 45% of its normal schedule in the fourth quarter. and it continues to forecast a 67% decline in revenue compared with last year's fourth quarter.

Southwest officials said bookings are rising for the holidays but so are cancellations — they didn't provide numbers for either.

When the holidays are over, leisure travelers will have even less reason to fly.

“I'm not real optimistic that the first quarter is going to improve much from the current levels of demand,” said Southwest CEO Gary Kelly. “It will be winter time, and we've already seen seasonally the uptick in the cases, and that's concerning.”

Kelly made the comments to reporters as he and other executives detailed Southwest's plans to bring the Boeing 737 Max back into the schedule, possibly in April.

On Wednesday, the Federal Aviation Administration approved an order ending the grounding of the plane once airlines update flight-control software and give pilots more training. All Max jets around the world were grounded in March 2019 after two crashes killed 346 people.

American Airlines plans to be the first U.S. carrier to begin using the Max, with once-a-day flights between New York and Miami scheduled to start Dec. 29. United expects to resume Max flights in the first quarter, followed by Southwest.

All three airlines say Max flights will be identified when customers book flights.

“We will call it out very clearly, it's a 737 Max 8. There is no hiding the ball,” said Southwest President Tom Nealon.

The airlines say they will let customers change flights if they want to avoid flying on a Max.

Moody’s Investors Service said air travel demand will be squeezed and the industry will continue losing money into 2022. Moody’s gives investment-grade credit ratings to only six of the 25 airlines it covers, including Southwest and Delta Air Lines.