For thousands of passengers, a seven-day cruise around the Caribbean has turned into floating nightmare after it was discovered a Texas health care worker on board is believed to have handled specimens from an Ebola patient who later died from the virus.

After being turned away in Belize, the Carnival's Magic ship, with more than 4,000 on board, headed to Cozumel, Mexico, where officials denied authorization for a scheduled port visit. Carnival is offering guests a $200 per person credit to their shipboard accounts, and 50 percent discount for a future cruise based on the missed visit to Cozumel, according to a statement. The ship had also stopped in Belize but officials there would not allow the passenger to leave the vessel. In a statement, the Belize government said it had refused a U.S. government request to fly the woman home through the Belize City airport. Other passengers were allowed to disembark there.

The ship is now headed back to Galveston, Texas, and is expected to arrive Sunday, the statement said.

The unnamed health care worker from Texas Health Presbyterian Hospital -- where Liberian national Thomas Eric Duncan was treated before his death -- boarded the ship on Oct. 12.

The health care worker was identified Wednesday through the Centers for Disease Control and Prevention’s (CDC) effort to track everyone who came into contact with Duncan, who died Oct. 8 after infecting at least two nurses who are currently hospitalized and receiving treatment.

The worker has been in voluntary isolation in a cabin along with her travel companion, and has not shown any possible symptoms of Ebola, the State Department said.

"The employee has been self-monitoring, including daily temperature checks, since Oct. 6, and has not had a fever or demonstrated any symptoms of illness," State Department spokeswoman Jen Psaki said in a statement. "It has been 19 days since the passenger may have processed the since deceased patient’s fluid samples."

Psaki said a doctor aboard the ship has monitored the woman and confirmed she is in good health.

"At no point in time has the individual exhibited any symptoms or signs of infection and it has been 19 days since she was in the lab with the testing samples," Carnival said in a statement. "She is deemed by CDC to be very low risk. At this time, the guest remains in isolation on board the ship and is not deemed to be a risk to any guests or crew. It is important to reiterate that the individual has no symptoms and has been isolated in an extreme abundance of caution. We are in close contact with the CDC and at this time it has been determined that the appropriate course of action is to simply keep the guest in isolation on board."

Officials said the lab worker did not have direct contact with Duncan, but may have had contact with clinical specimens collected from him. At the time the woman left on the cruise, the CDC was requiring medical workers involved in treating Duncan to self-monitor and was not restricting their travel. It has since updated requirements for active monitoring.

When the ship stopped in Belize, the other passengers were allowed to disembark.

"The government of Belize reassures the public that the passenger never set foot in Belize and while we remain in close contact with U.S. officials we have maintained the position that when even the smallest doubt remains, we will ensure the health and safety of the Belizean people," the government said in a press release.

The statement added that the passenger is "considered of very low risk for Ebola,” but "nonetheless, out of an abundance of caution, the Government of Belize decided not to facilitate a U.S. request for assistance in evacuating the passenger through the Phillip Goldson International Airport.”

Two nurses who treated Duncan at the hospital, Nina Pham and Amber Vinson, have been diagnosed with Ebola. Pham was flown on Thursday to the National Institutes of Health facility in Bethesda, Md., and is recovering. Vinson, who got clearance from the CDC to take a domestic flight from Cleveland to Dallas despite advising officials she had a temperature, is being treated at Emory Hospital, in Atlanta.

On Friday, sources said the condition of all four Ebola patients in the US is “stable.”

The disease has killed more than 4,000 people in West Africa, with most of the deaths coming in the nations of Liberia, Sierra Leone and Guinea.

The Associated Press contributed to this report