MIAMI (CBSMiami) – The number of coronavirus cases on cruise ships continues to climb sharply. That has managers of cruise lines with headquarters in Miami-Dade County keeping their eyes on its spread.

Thousands of passengers to and from PortMiami and Port Everglades have been safe daily. But around the world, there’s been a greater threat and concern.

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Thirty-six hundred passengers have been isolated on Diamond Princess. It’s docked near Tokyo and has been there for more than a week. Americans were on that cruise that turned into a floating incubator.

“It was a very surreal experience to be told that you have this virus, as far as I know, could be deadly,” Rebecca Frasier said.

Frasier, a resident of Oregon, is the first person with the virus to go public. She spoke to CBS News from her hospital bed.

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The latest numbers show 23 American passengers contracted the illness. Video showed crews wearing protective gear to escort those who are sick off the boat.

Thousands have been send to pop-up hospitals and quarantine centers. More than 40,000 globally have been infected, but most are in China.

U.S. officials confirmed to CBS News Monday there are 13 cases in America.

Symptoms are described as a fever or flu-like. Some can get life threatening illnesses such as pneumonia.

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As for the Diamond Princess, it’s operated by Princess Cruises. Its parent company is Carnival Corporation.