For the cruise industry, the coronavirus is a public-relations nightmare.

For more than a week, the world has watched as the Diamond Princess ship has been quarantined in the Japanese port of Yokohama, its 3,600 passengers and crew stuck and the number of people infected by the coronavirus climbing to at least 175.

A second ship has been sailing the South China Sea like a modern-day version of the Flying Dutchman, turned away from five ports over fears that a person onboard was infected.

Even thousands of miles from the outbreak, in Bayonne, N.J., four Chinese passengers aboard a cruise liner were briefly quarantined after health officials screened more than two dozen passengers. They turned out not to have the coronavirus.

The cruise lines have faced crises before, from their ongoing battles with the norovirus, which can tear through an entire boatload of passengers causing gastrointestinal problems, to the 2012 sinking of the Costa Concordia, whose captain ran it aground off the coast of Italy, killing 32 people. But COVID-19, as the virus has been named, and whose ultimate worldwide spread is still to be seen, could be its biggest challenge yet.

“The longer ships like the Diamond Princess stay in the press, the more people who have never taken a cruise before think of cruising as a less than ideal vacation,” said James Hardiman, the managing director of equity research for Wedbush Securities, who follows the industry.

The cruise companies have been reluctant to release any data about whether there has been any impact on bookings in the $45.6 billion global industry in the weeks since the outbreak began in the Chinese city of Wuhan, but some travel advisers say they are off by 10 to 15 percent.

The companies, including the biggest lines like Norwegian Cruise Lines and Carnival Corp., which includes Princess Cruises, have either declined to comment or have released statements reiterating that their priority is passenger safety. Each cruise line also listed the precautions it is taking to keep passengers safe: Because they typically have thousands of people in a small space over an extended period of time, cruise ships are known to be incubators for illnesses.

Royal Caribbean offered a glimpse into the situation in a Feb. 4 statement, but would only go so far as to say, “the Wuhan Coronavirus and the efforts to contain it are expected to negatively affect our results.” The company, whose ship was briefly stopped in Bayonne, announced that no one with a Chinese passport would be allowed to embark on a Royal Caribbean cruise, a decision later rescinded after an outcry.

But Erika Richter, the senior director of communications for the American Society of Travel Advisors, an industry group, said that demand for cruises, which had been on an upward trajectory before news of the coronavirus broke, was off from 10 to 15 percent according to some advisers.

  • What do you need to know? Start here.

    Updated Feb. 10, 2020

    • What is a Coronavirus?
      It is a novel virus named for the crown-like spikes that protrude from its surface. The coronavirus can infect both animals and people, and can cause a range of respiratory illnesses from the common cold to more dangerous conditions like Severe Acute Respiratory Syndrome, or SARS.
    • How contagious is the virus?
      According to preliminary research, it seems moderately infectious, similar to SARS, and is possibly transmitted through the air. Scientists have estimated that each infected person could spread it to somewhere between 1.5 and 3.5 people without effective containment measures.
    • How worried should I be?
      While the virus is a serious public health concern, the risk to most people outside China remains very low, and seasonal flu is a more immediate threat.
    • Who is working to contain the virus?
      World Health Organization officials have praised China’s aggressive response to the virus by closing transportation, schools and markets. This week, a team of experts from the W.H.O. arrived in Beijing to offer assistance.
    • What if I’m traveling?
      The United States and Australia are temporarily denying entry to noncitizens who recently traveled to China and several airlines have canceled flights.
    • How do I keep myself and others safe?
      Washing your hands frequently is the most important thing you can do, along with staying at home when you’re sick.

Not surprisingly, cruises in Asia and the Pacific were especially hard hit. Alex Sharpe, president and chief executive of Signature Travel Network, a consortium of 7,000 travel advisers said, “New demand for these cruises is very low currently” and that spring sailings were “unlikely to sell from our market.”

“If the industry doesn’t get its arms around this it could affect customer confidence in China toward cruises for a very long time,” said Mr. Hardiman, of Wedbush Securities.

China has been one of the travel industry’s biggest growth markets in recent years, and, trips in the Asia-Pacific region make up about 10 percent of the industry, according to the Cruise Lines International Association, a trade group. Between 8 and 9 percent of passengers on cruise lines represented by the trade group are from China, Macau or Hong Kong and the number of ships deployed in Asia grew 53 percent between 2013 and 2017.

A growing number of ports across the Pacific, from Busan, South Korea to the New Caledonian ports of Lifou, Mare and Isle of Pines, are banning cruise ships. Hong Kong has been closed since Feb. 6.

Passengers say that rather than trying to accommodate them, the cruise companies have been uncommunicative and unhelpful. Maranda Priem, 24, of Washington, D.C., and her 53-year-old mother, from Minnesota, were supposed to be aboard the Norwegian Jade, a 2,200-passenger ship operated by Norwegian Cruise Lines, which was originally scheduled to depart from Hong Kong on Feb. 17 for a cruise stopping in Singapore, Vietnam and Thailand.

As her concerns about the coronavirus grew, Ms. Priem repeatedly emailed and called the company asking if she could switch to a different cruise or receive a refund or future credit. Her requests were denied. In an email on Feb. 4, Roxane Sanford, coordinator of guest relations for the cruise line, reminded Ms. Priem that “mainland China does not include Hong Kong, Macau or Taiwan,” and added that, “Regrettably we are unable to proceed with cancellation and refund.”

When the Hong Kong port closed, the company moved the sailing to Singapore, a change in itinerary that required Ms. Priem and other passengers to rebook their flights and absorb any extra costs. On Wednesday she decided to cancel, without knowing if she will get the nearly $1,700 she paid for the cruise back.

“It’s been a bit of a nightmare dealing with Norwegian,” she said. “Norwegian won’t tell us what they will reimburse and they haven’t been helpful.”

Norwegian Cruise Line did not respond to requests for comment.

When a ship’s itinerary is changed, “passengers have little recourse as a practical matter,” said Jim Walker, a maritime lawyer who represents people suing cruise lines. “Cruise lines are able to freely alter their itineraries and if you don’t have insurance you’re just stuck, and the trouble with insurance is it often has exceptions for pandemics and things like this.”

Mr. Walker said that he has received a “significantly higher” volume of calls from travelers looking for guidance on how to deal with cruise lines changing itineraries without offering refunds or the chance to reschedule.

Cruises tend to be expensive, with an average nine-day sailing in Asia running about $1,800, travel advisors said, and booked long in advance. Angela Jones, 56, from Canton, Ga., a passenger on the MS Westerdam, the Holland America ship that was stuck in limbo looking for a port that would take it, booked her trip a year and a half ago.

When news about the coronavirus broke, her daughter, Jordan Jones Dorman, said on Tuesday, “She considered canceling, but the company said repeatedly that they’d be OK and wouldn’t offer a refund if she canceled. She’d been saving up for this trip. Hindsight is 2020, but why was the cruise still happening?”

Sihanoukville, in Cambodia, finally agreed to let the ship dock on Wednesday. Holland America Line said that it will arrange and pay for all passengers’ flights home, in addition to giving a full refund for the cruise.

Mr. Hardiman, of Wedbush Securities, estimated that it cost Royal Caribbean about $4 million to cancel a recent four-day cruise, a number that could differ depending on ship size and other factors.

“Cruise companies have never seen this before and just don’t know what to do,” said Ross Klein, a sociologist at Memorial University of Newfoundland who studies the cruise industry. “For the cruise lines and the industry a lot of these decisions are based on economics. They are asking themselves, ‘How do we get by spending the least amount of money and losing the least amount of money?’”

David Yaffe-Bellany and Niraj Chokshi contributed reporting.