Wuhan, China — Chinese authorities said Tuesday that the outbreak of a new coronavirus centered in the city of Wuhan has now claimed the lives of six people. The mayor of Wuhan told China's state broadcaster CCTV that there had been a total of 258 confirmed cases of the illness in his city, including 227 people who were still receiving treatment.

Travelers and residents were stepping up precautions after officials confirmed on Monday that the pneumonia-like virus can pass from person- to-person. That has heightened fears that the epidemic could spread much more quickly, and much further.

CBS News correspondent Ramy Incocencio said officials in Wuhan have designated nine hospitals as treatment centers — that's on top of 61 fever clinics and a team of medical experts dedicated full-time to combating the outbreak.

One bit of good news came as Chinese scientists said they had determined the DNA sequence of the new coronavirus. That could help in the development of treatments, and potentially a vaccine, as the virus threatens to spread even more rapidly.

The specter of a larger outbreak looms as hundreds of millions of Chinese make their way across the country, and travel back to it from abroad, to ring in the lunar new year.

As China and nearby nations deal with the massive challenge of stemming the outbreak, travelers wearing masks, quarantine stations and temperature checkpoints are becoming common sights at airports and other travel hubs across Asia.

Eric Rubin, Editor-in-Chief of the New England Journal of Medicine, says as the nation at the center of the epidemic, "China has the primary role in gathering information," and he said the country's local and national health authorities had thus far "done a very responsible job."

The number of known infections has risen sharply since Monday, topping 300 across China alone. A few cases have been confirmed elsewhere in Asia, the latest being a woman who recently returned to Taiwan after visiting Wuhan.

"So far four cases have been reported outside China, two in Thailand, one in Japan and one in the Republic of Korea (South Korea)," World Health Organization spokesperson Tarik Jasarevic said Tuesday, before the Taiwan case was reported. He added that "more cases should be expected in other parts of China and possibly other countries in the coming days."

At least 15 hospital workers in Wuhan have been diagnosed with the virus — none of whom were believed to have been directly exposed to the city's seafood and animal market, considered ground zero for the epidemic.

A store owner argues with security guards as he attempts to enter the closed Huanan wholesale seafood market in the city of Wuhan, Hubei province, January 12, 2020. NOEL CELIS/Getty

"If in fact a person who is infected has infected a healthcare worker, that's obviously of some concern," Dr. Anthony Fauci, Director of the National Institute of Allergy and Infectious Disease at the National Institutes of Health, told CBS News.

Fauci said the human-to-human transmissions could be isolated incidents, but "when you get sustained transmissibility from one person to another to another to another, then you have a more serious problem because then that would allow for a much broader type of an outbreak."

The World Health Organization has said it will assemble an emergency committee of experts, expected to meet Wednesday to decide whether the outbreak yet constitutes a global emergency, and how to contain it.