A California passenger aboard the Diamond Princess told CNBC on Monday it "can be a little bit depressing" when thinking about how much longer he and his wife must remain on the quarantined cruise ship: likely nine more days.

Matthew Smith, 57, told CNBC's "Squawk Box" he is "maintaining his confidence" that he and his wife, Katherine, will not test positive for the new coronavirus and be able to go home after the two-week mandatory quarantine on the cruise ship ends.

"Imagine being trapped in your bathroom," said Smith, explaining what life is like for some passengers over the last few days.

The Diamond Princess cruise ship, which is operated by Carnival's Princess Cruises, is carrying about 3,700 passengers and crew at the port of Yokohama, south of Tokyo. The company announced last week that it was quarantining the ship for two weeks after a previous guest, who didn't have any symptoms while aboard the ship, tested positive for the coronavirus.

On Monday, Princess Cruises confirmed an additional 66 cases of the flu-like virus, bringing the total number of people infected to 136.

Coronaviruses are a large family of viruses that usually infect animals but can sometimes evolve and spread to humans. Symptoms in humans include fever, coughing and shortness of breath, which can progress to pneumonia.

World health officials know the respiratory disease is capable of spreading through human-to-human contact, droplets carried through sneezing and coughing, and germs left on inanimate objects. The illness is capable of spreading before symptoms show, and about 20% of patients become severely ill, leading to pneumonia and respiratory failure, health officials say.