Measles is highly contagious and can be transmitted via the air through sneezing or coughing, or by physical contact with an infected person or with an object that the person has touched.
"One infected person can easily infect others", she said in a public statement. The ship's doctor is now monitoring the condition of the ship's crew and passengers.
"The ship is free to leave our port anytime it wishes", she said.
According to Reuters Eikon shipping data, a Panamanian-flagged cruise liner identified as SMV Freewinds was docked in port near Castries on Thursday. An unidentified person who answered the phone at the church's media centre said no one was immediately available for comment.
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Measles outbreaks, which the CDC defines as three or more cases, are now ongoing in New York, Michigan, New Jersey, California, Georgia and Maryland, and many are linked to people traveling overseas to places like Israel and the Philippines, where measles outbreaks are occurring.
Fredericks-James says the decision to quarantine the cruise vessel was informed in part by news of the rapid spread of measles in parts of the United States. She pointed to measles outbreaks in the U.S. as the primary motivation for taking the extreme step of caution.
Officials said the increase in cases is the largest since 1994, including 78 reported in the past week.
Every state has laws in place that allow quarantines and other public health enforcement tools, and they differ based on the jurisdiction.
Though some high-profile Scientologists have come out against vaccinations, the church has not taken a specific position on the issue.
The vast majority of USA cases have occurred in children who have not received vaccines against measles, mumps and rubella (MMR), officials said. Scientologists, according to the website, use prescription drugs when physically ill and "rely on the advice and treatment of physicians".