Christine Kim, one of Ms. Yu’s friends, said she understood her friend’s concerns but rebooked her own trip on Korean Air. She said she thinks some of the media coverage of the virus seems to be exaggerated.

“A lot of news stories are overblowing the danger of the virus, so it makes sense that people might not want to travel,” she said. “But as long as I’m not physically prevented from going, I’m not too worried. I’ve flown Korean Air and trust them.”

For other travelers, it’s been unclear who exactly is responsible for issuing refunds.

Laura Clews had a China Eastern Airlines flight to New Zealand from London, with a stopover in Shanghai. When the flight was canceled last week, Ms. Clews spent several days trying to get in touch with the airline, ultimately learning that she would have to get a refund through the site she booked on, Travel Genio.

“I went to the Travel Genio site to see if they would be honoring what China Eastern said, but there wasn’t anything on the site, so I found a number for them and tried calling six times,” she said.

No luck. Ms. Clews has since reached out to Travel Genio by phone and email, as well as on Instagram, on Facebook and, with a newly created account, on Twitter. She hasn’t heard back.

Attempts to contact the company by phone and through social media for comment were unsuccessful.

Jayne and Ed O’Donnell had planned to visit their daughter and son-in-law in China, where they both teach science in Shanghai. Their monthlong trip was going to take them to Vietnam, Laos and Cambodia as well.