The coronavirus has hurt all travel-related companies, but cruise ship operators have been especially hard-hit, thanks to news and images of passengers quarantined in the Port of Yokohama, Japan, or stranded at sea, looking for a port to accept them.

Although stocks in the big three cruise ship operators have gotten slammed this year, the companies have yet to offer significant price cuts, but that could change if the virus, now called COVID-19, is not quickly contained.

“Our Asia cruise business stopped overnight,” said Jay Johnson, owner of Coastline Travel Advisors in Orange County. His sales overall are off 5% this year compared to the same period last year. Cruise bookings are down more than that, everything else is up.

“People who have cruises booked to Asia for the next few months are asking for cancellations.” Right now most cruise lines are not allowing refunds but will let them rebook a different cruise, he said.

Many cruise lines have canceled or rerouted ships calling on ports in mainland China, Hong Kong, Macau and some other Asian countries through mid-March. Passengers on canceled trips have been offered full refunds and credits for future travel. For everyone else, there is no single policy, said Chris Gray Faust, managing editor with CruiseCritic.com, which has been tracking ships in the region.

The only ship with confirmed coronavirus cases is the Diamond Princess, owned by Carnival. It has been docked at the Port of Yokohama since Feb. 4 with 2,666 passengers. Japan’s health ministry said 174 of them are infected.

Johnson’s clients Carol and Otis Menasco of Granite Bay are on board the ship. “We are very isolated, confined to our cabin,” Carol said via email. Passengers are allowed on the deck in rotating shifts for about 1½ hours every other day, but “we do not go out as we have a balcony” and that feels safer. The crew “is treating us well.” They deliver a “limited food selection to our door. They are not allowed to come in. We did run out of our medications and my husband had to get pretty aggressive to get refills.” The couple has been on about 20 cruises, “but will stay away from Asia now,” Carol said.

“We understand the quarantine but this is very hard to miss two weeks from your home that you didn’t plan on. We have two cats that will have been boarded five weeks by the time we get home and we have missed many appointments,” she added.

Holland America’s Westerdam departed Hong Kong on Feb. 1 with scheduled stops in Taiwan and Japan. It was supposed to end in Yokohama on Feb. 15, but on Feb. 6, the company said Japan banned it from all Japanese ports. It was also denied entry in Taiwan and South Korea and rejected by ports in Manila and Guam, according to CruiseCritic.com.

It was supposed to dock in Bangkok Thursday, but now that is uncertain.

Christina Kerby, a public relations executive with Blue Shield of California in Oakland, has been tweeting about her experience onboard the Westerdam and posting pictures of spin classes and other activities to “show that the passengers are upbeat and going about our lives as normally as possible,” she said via LinkedIn.

Johnson has other clients aboard the Crystal Symphony, which left San Diego Jan. 13 and was traveling the Pacific islands and Vietnam. It picked up passengers in Guam on Feb. 1, said Lea Bregner, their travel adviser.

It was supposed to end in Hong Kong Feb. 15, but that port has been closed. It’s now scheduled to dock in Singapore Wednesday. The passengers are not quarantined, there are no cases of coronavirus and there are plenty of food choices, Bregner said. The boat stopped to dump sewage and take on extra fuel “to cover floating aimlessly.”

Shares in Carnival and Royal Caribbean Cruises, the two biggest operators, which each own numerous brands, are down more than 15% this year, compared to a 4% return for the S&P 500.

Cruises that leave and return from China make up only 5% and 6% of their total trips, respectively, said Patrick Scholes, an analyst with SunTrust Robinson Humphrey. Shares in Norwegian Cruise Line Holdings are down about 10% even though China accounts for less than 0.2% of its trips.

As of Feb. 4, Royal said it had canceled eight cruises out of China through March 4. Carnival hasn’t quantified its cancellations, but a trade magazine reported that it had canceled nine in the Costa line as of the end of January, Scholes said.

Cancellations “can have a disproportionate impact on earnings. If the cruise gets canceled on short notice, they are not going to get rebooked,” Scholes said. Their crews are usually on six- to 12-month contracts and get paid even if there are no passengers. There is also some food spoilage, extra fuel if the ship is rerouted and “loans for the ship still have to get paid.”

Tuna Amobi, an analyst with CFRA Research, downgraded Royal Caribbean and Norwegian this week. “We are wary that this could have an impact not just on Chinese travel but on other key markets like the U.S. and Europe,” he said.

All cruise lines that belong to the Cruise Lines International Association have adopted passenger-screening measures developed by the association. These include denying boarding to all persons who have traveled from, visited or transited via airports in China, including Hong Kong and Macau, within 14 days before embarkation. They also say to deny boarding to anyone who, within 14 days of embarkation, had close contact with anyone suspected or diagnosed as having the coronavirus.

January through March is known as wave season, when cruise lines try to fill their ships during the crucial summer months by offering extras such as booze packages, free Wi-Fi or shore excursions. That’s going on now.

But apart from some softness in Asian pricing, there has not been any widespread discounting yet, said Morningstar analyst Jaime Katz.

Gabe Saglie, senior editor with the website Travelzoo, said that Carnival “is seeing some cancellations. People staying on are getting upgraded,” but overall prices haven’t fallen. Avid cruisers “are going to wait to reschedule that Asian cruise, or put their cruise dollars into another destination.” The industry “may see a bit of a pullback” among people who would have taken their first cruise in 2020.

Cruise lines aren’t jumping to cut prices because coming into the year, demand was strong. “It was looking like 2020 could be a record year before this outbreak,” Amobi said. If the epidemic ends soon, there’s no need to cut prices for summer travel.

The SARS outbreak in 2003 impacted the industry, “but nothing on this level, with quarantines,” Amobi said.

The incident that had the biggest impact was the sinking of the Costa Concordia off the coast of Italy in 2012, which killed 32. The hulk of the ship could be seen for more than a year, serving as a grim reminder of the disaster.

The next year, a fire knocked out power on the Carnival Triumph, and more than 4,000 passengers and crew were stranded at sea for days, mostly without air conditioning and working toilets, before it was towed into Mobile, Ala. The journey came to be known as the “poop cruise.”

“Those two events hurt cruising in general,” Scholes said. “People were saying, you can’t pay me to take a cruise,” and prices fell. “It took two to three years to see the cruise lines start to recover. Carnival suffered the most.”

The coronavirus outbreak is so fluid that no one is hazarding a guess when it will end or where it will lead for the industry.

Kathleen Pender is a San Francisco Chronicle columnist. Email: kpender@sfchronicle.com Twitter: @kathpender