The hantavirus outbreak aboard the MV Hondius "is on the end of its run right now," a top infectious disease expert told ABC News "This Week" Sunday.

"The good news is that, in a sense, it is hantavirus and not another coronavirus or influenza virus. This is one that has very limited ability to be transmitted person to person. In fact, it's a rare exception," Dr. Michael Osterholm, director of the University of Minnesota's Center for Infectious Disease Research and Policy (CIDRAP), told ABC News' Martha Raddatz. "And so we have no question about the fact that this really is on the end of its run right now."

There are about 30 cases of hantavirus a year in the U.S. on average, and "they mostly occur west of the Mississippi" – about 96%, Osterholm said, due to a specific mouse that lives in that region. He also said that person-to-person transmission of the hantavirus strain in question is "a very rare exception," and only occurs when someone is exhibiting symptoms of the virus.

"Right now, you can manage the individuals who have been exposed very simply by asking them twice a day, 'are you experiencing any kind of a fever?' And then take the temperature: 'Do you have any symptoms?' If somebody is identified right at that point, you can put basically an N95 mask on and stop all transmission," Osterholm said.

"So this is why we don't need this high-tech, you know, containment facilities, et cetera, to monitor these people. We can monitor them very simply," Osterholm added, explaining why quarantining returning Americans isn't necessary.

"I have complete confidence that we will have good compliance here," Osterholm said of monitoring passengers who are returning. "And I think within days, this will no longer be a story."

-ABC News' Quinn Scanlan

An airplane from the U.S. is expected to land in Tenerife, in the Canary Island, at 5:23 p.m. local time/12:23 p.m. Eastern time, according to a source in the Spanish president's office.

The aircraft will carry U.S. passengers only, according to the source. There are 17 U.S. citizens aboard the ship who will be returning to the United States.

As of now, the U.S. airplane is expected to take off from Tenerife at 9:30 p.m. local time/4:30 p.m. Eastern time but could possibly depart earlier if circumstances allow, the source said.

The passengers onboard the MV Hondius began disembarking from the ship in Tenerife on Sunday morning.

-ABC News' Aicha El Hammar

"The average person has no reason to worry" about potential hantavirus infection, according to an expert with the World Health Organization (WHO).

"This Andes hantavirus has spread in limited amount from human to human ... This is not COVID, this is not passing someone in a hallway in an airport outside at a stadium and getting infected," Dr. Boris Pavlin, an epidemiologist and the team lead for Field and Humanitarian Epidemiology at the WHO, told ABC News.

He also said the investigation in the hantavirus infection cluster's origin indicates "there's absolutely every reason to believe that this came from rodents" and that it did not originate from the region the ship departed, but elsewhere in northern Argentina and Chile, where the long-tailed rice rat, which is the specific carrier of the Andes hantavirus strain, is common. Pavlin also confirmed that the first hantavirus cases on board the MV Hondius had previously traveled to this region in the north.

Pavlin additionally confirmed that no one on board was currently showing any symptoms but were "just being monitored as a precautionary measure." He also said he understands why people are concerned.

"I know it's a new name for a lot of people, but this is not a new virus. We've known about it for decades and it's not surprising us," Pavlin said.

-ABC News' Maggie Rulli, Dragana Jovanovic and Aicha El Hammar

Passengers onboard the MV Hondius began disembarking in small groups on Sunday morning, heading for the shore in Tenerife, where they were expected to continue on to charter flights back to their home countries.

Spain’s health minister, Monica Garcia, who was at the port in the Canary Islands on Sunday, said the remaining passengers were all thought to be asymptomatic.

"The entire operation is proceeding normally and I said the first to disembark will be the Spanish citizens, and then the flight to the Netherlands will depart," Garcia said prior to the passengers' beginning of their departures from the ship.

Flights were planned for passengers who were headed to Canada, Turkey, France, Great Britain, Ireland and the United States, she said.

"The Netherlands will send two planes: today's plane and another one tomorrow, which we'll call a 'sweeper plane,' to pick up any passengers not picked up by the other countries," she said. "But in principle, well, throughout today and tomorrow, all the planes of all nationalities will be disembarked and taken back to their respective countries."

-ABC News' Rashid Haddou and Maggie Rulli

Fifteen passengers were welcomed to the University of Nebraska Medical Center’s quarantine unit Monday morning and one person who tested positive is in the biocontainment unit, according to officials.

The quarantine unit is more like a hotel, while the biocontainment unit is patient-based care, more like a hospital, officials said.

The 15 passengers at the quarantine unit are in “good spirits,” the unit’s medical director, Dr. Mike Waldman, said.

“We’ve been doing symptom monitoring, as well as temperature checks," he said. "Everyone here is asymptomatic and ... do not have a temperature at this time. They're all resting now and we'll do further assessments later in the day, once they've had a chance to sleep."

The one person in the biocontainment unit is doing well and does not have symptoms, but is “very tired” after a “really long journey,” officials said.

The 15 in the quarantine unit will have the option to stay in Nebraska at the quarantine center for the entire 42-day monitoring period, or go home to monitor symptoms, in coordination with their state and local health departments, officials said. This will be based on whether they develop symptoms, have a support structure at home to quarantine and can contact their health department, officials said.

Besides the 16 cruise ship passengers in Nebraska, two cruise ship passengers -- who are a couple -- were flown to Atlanta “for further assessment and care," officials said. At least one of the two in Atlanta had symptoms, officials said.

The two patients in Atlanta "are under medical evaluation" at Emory University’s Serious Communicable Diseases Unit, officials said, noting that their transfer there was "contingency planning."

"That means, if we're on it, since there was symptoms involved, they want to make sure that if they turn out to actually have the hantavirus, that it makes sure that the biocontainment unit here that provides medical care doesn't take up too much space, in case it's needed by the other passengers who are currently here in the more residential section," officials said.

The Georgia Department of Public Health said, "There is no risk to the public at this time. ... DPH is also remaining actively in communication with the CDC and other partners and will continue to do so for as long as necessary as we monitor each development in the coming days and weeks.”