At the outset of this year, as U.S. coronavirus cases were falling from their winter peak, still nearly 80% of Americans had recently delayed at least one medical service, according to a Time-Harris poll conducted in February.

The trend left hospitals with fewer patients and insurance companies with fewer claims. But in a sign of the nation's return to normal, Aflac (AFL) CEO Dan Amos tells Yahoo Finance he expects claims to reach pre-pandemic levels by the latter part of this year.

Moreover, Amos said the company may see a surge in claims as patients schedule long-postponed doctor's appointments and some discover advanced illnesses that require costly treatment.

"It's coming back," he says. "What we said in our [first quarter earnings] conference call was we expected claims to recover, go back to normalcy of what they were in 2019 within certainly by a quarter of the second half of the year."

"We're just not sure if we're still going to have more claims," said Amos, who has led the company since 1990. "We're not sure yet how much is out there in the future claims that will come."

Shares of insurance companies MetLife (MET), Prudential (PRU), and Aflac plummeted with the onset of COVID-19 in the U.S. last spring. But they rebounded in recent months on declining coronavirus cases and reduced insurance claim payouts.

In the first quarter, Aflac continued to experience a low level of paid claims for medical conditions other than COVID, since policyholders largely avoided routine hospital visits, Aflac President Frederick Crawford said in April on the company's earnings call.

But the level of claims showed signs of a return to normal over the first quarter, the company said.

For example, in January the company saw paid claims in the U.S. drop about 28% compared to pre-pandemic conditions, Max Broden, Aflac Executive Vice President and CFO, said on the earnings call. But "we saw a significant normalization from that level in the month of February and further normalization in the month of March," he noted.

Amos, whose father Paul Amos co-founded Aflac, began at the company in 1973 as a regional sales director. In the ensuing years, he climbed the ranks as president and then CEO. In 2001, he was also named the company's chair.

Speaking to Yahoo Finance, Amos explained how delayed treatments could cause a spike in claims for expensive treatments.

"I have a friend whose wife was diagnosed with cancer, but she couldn't go last year. And when she finally was able to go, just to have a chat, regular checkup, it had moved from what would have been an early stage one to a stage three," he says.