The report says the ship has been quarantined since Monday, when the case was confirmed in a female crew member who is being held in isolation on the ship.
Frederick-James said the doses of measles vaccines were being supplied to the ship free of charge.
SAN JUAN, Puerto Rico - Authorities on the eastern Caribbean island of St. Lucia said Thursday that they quarantined a cruise ship with some 300 people aboard after discovering a confirmed case of measles aboard.
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Fredericks-James said no one was allowed to disembark from the ship.
An unidentified person who answered the phone at the church's media center said no one was immediately available for comment.
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.
The Church of Scientology has not officially published a stance on vaccines, and does not prevent followers from following doctors advice or taking medicine. For a Scientologist, boarding the ship is "the most significant spiritual accomplishment of his lifetime and brings with it the full realization of his immortality". Home of the Flag Ship Service Organization (FSSO), the Scientology website touts it as a "religious retreat ministering the most advanced level of spiritual counseling in the Scientology religion".
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We wish to remind persons that there are now large measles outbreaks in some countries.
Though some high-profile Scientologists have come out against vaccinations, the church has not taken a specific position on the issue.
With measles cases growing quickly, many adults are now wondering if they were vaccinated as children.
The United States is current experiencing once of the worst measles outbreaks in years, since the disease was reported as "eliminated" in the year 2000, according to CNN.
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Preliminary global data showed that reported cases of measles have been up almost 300% in the first three months of 2019 compared to the same time frame in 2018, according to the World Health Organization.