The Ocean Explorer, a cruise ship, carrying 206 passengers and crew, with three of them testing COVID-19 positive, ran aground on a remote stretch of Greenland earlier this week.
According to reports, the luxury ship might remain stranded in the area for days.
Tour agency Aurora Expeditions, which operates the ship, said the infected people have been kept in isolation and other passengers are currently healthy and safe.
Lis, a passenger on the cruise ship, told CNN affiliate Nine News she felt the Covid situation was “contained” and that her biggest fear at the moment is running out of alcohol.
“That is the biggest concern I have,” she said.
Sharing her backup plan if such a situation emerges, she said: “I had swimming lessons before I came and I’m a good swimmer.”
Lis said, “So look out, I could be swimming back to Iceland.”
Denmark’s Joint Arctic Command issued a statement on the crisis and said: "On Monday afternoon, the cruise ship Ocean Explorer ran aground in Alpefjord, which is located in the national park in the northeast of Greenland, just over 600 km north of the Arctic Circle."
"Since then, the ship has unsuccessfully tried to free itself," the statement said.
Rescue vessels from Danish Defence have been dispatched to the scene.
"Arctic Command has also dispatched other forms of assistance to the cruise ship. Yesterday Tuesday 'Luftgruppe Vest' flew over the cruise ship with a Challenger surveillance plane. Pictures of the ship were taken from the plane," the statement said.
"The pictures can help assess the situation on-site. The inspection vessel Knud Rasmussen has also been sent towards the cruise ship," the statement said.
Joint Arctic Command said after the incident, the inspection vessel Knud Rasmussen, was dispatched to assist the cruise but it had to cover 1,200 nautical miles - just over 2,200 km- to reach the ship.
According to the official website of Aurora Expeditions, the ship was 'purpose-built for expedition travel to the world’s most remote destinations'.