The air travel industry is “not quite out of the woods” — but the future could be brighter than the last 20 months, says Paul Griffiths, the chief executive of Dubai Airports.

“We have room for optimism that the future, hopefully, is much brighter than the last 20 months,” he told CNBC’s Dan Murphy on Sunday at the Dubai Air Show, the first major international air show since the Covid pandemic began.

The city’s airports have seen 20.7 million passengers this year, a “far cry” from pre-pandemic levels, which may only be achieved in 2025, he said.

But there are signs of recovery as the world relaxes restrictions and major international traffic flows start up again, he said. Traffic numbers at Dubai International grew 40% in the last six weeks, he added.

Dubai Airports owns and manages Dubai International and Dubai World Central Airports in the United Arab Emirates. Dubai International alone served 86.4 million customers in 2019.

By the end of this year, Griffiths expects Dubai Airports to see 26.7 million passengers. That figure could jump to 56 million or 57 million in 2022, he said.

The CEO said he’s cautiously optimistic that passenger numbers could be even better.

“I do hope that there is a case for slightly more optimistic forecasts, but we’re in unknown territory,” he said.

Dubai International is “very aggressively” getting back to normal operations after a period of “hibernation,” he told CNBC. “We’re very optimistic that we will lead the recovery and the world will be traveling again very shortly.”

Asked about the biggest threats to air travel recovery, Griffiths said the risk of a surge in Covid infections leading to lockdowns is a “big problem.”

Just this weekend, the Netherlands returned to a partial lockdown as soaring Covid cases stretched capacity at hospitals.

Griffiths added that many people likely do not have the confidence to travel because of strict regulations, expensive Covid testing protocols and the fear of rules changing quickly.

“The last thing you want to do is embark on a journey and then get stuck somewhere having to quarantine,” he said, though he acknowledged that that is less of a risk now.

The economic situation — whether people have the disposable income to go on trips the way they used to — is another factor that will affect the recovery of the aviation sector, he said, but added that he is “fairly confident” about the demand.

“If airlines and airports respond with a quality product, and good value for money, people are so desperate to get back in the air again, they will respond,” he said. “We’re starting to see the green shoots of that already.”