Investors, optimistic that a COVID-19 pandemic recovery is underway, pushed airline stocks to 52-week highs this week.

But "the patient is still in intensive care," Airlines for America (A4A) President and CEO Nicholas Calio told Yahoo Finance Live. A4A is a trade group which lobbies on behalf of the biggest airlines in the country.

Recent trends show the industry beginning to recover from the pandemic. According to the Transportation Security Administration, more than 1 million people, on average, passed each day through the nation's airports between March 7 and March 15.

"With that said, we're still flying 50% less people than we used to," Calio pointed out. More than 2 million passengers a day passed through the nation's airports in 2019. That number fell 96% to about 100,000 a day during the worst of the pandemic.

Recent Securities and Exchange Commission filings from the airlines hint at cautious optimism that passengers are returning.

Southwest (LUV) says it sees increased bookings with beach and other "nature-inspired destinations" outperforming other regions. The airline's Form 8-K filing says operating revenues are expected to improve above Southwest's previous estimates but makes no long term projections that the trend will continue. "The Company has recently experienced an increase in bookings farther out in the booking curve, but currently has limited visibility to bookings beyond May 2021."

Similarly, the 8-K filing from Delta Air Lines (DAL) says “Domestic demand is improving across the booking curve. Bookings for travel departures beyond 60 days represent 32% of new bookings down only 3 points from 2019 compared to down 10 points in January.”

At United (UAL), the 8-K filing says the airline, "has seen improvement in customer demand for travel and new bookings compared to previous estimations in recent weeks. The Company now expects core cash flow for the month of March 2021 to be positive if the current trajectory of bookings improvement is sustained."

American Airlines (AAL) recently presented at the JP Morgan Industrials Conference and said it expects a "non-linear recovery with a quickening pace once we see widespread vaccinations and government restrictions ease." American has also added more flights to accommodate the increased passenger load.

"Our hope is that we're going to continue to see this uptick in the numbers," Calio said. "So we believe it is sustainable. But again, it's hard to forecast, this virus has been very tricky and we're hoping that we're making real progress against it. If that happens, the numbers will stay up."