Health authorities are concerned that a virus originating in central China could spread when hundreds of millions of Chinese travel during next week's lunar new year festival.
However, residents said there was little anxiety in the city at the epicentre.
Chinese officials are cracking down on those who spread news about the disease online, some people said.
As of Friday, two people in the city of Wuhan had died following an outbreak of pneumonia linked to a new strain of coronavirus that authorities suspect originated in a seafood market.
Wuhan's health authority said on Saturday that a further four people were confirmed to have the virus, bringing the total number of known cases to almost 50.
Two cases have been reported in Thailand and one in Japan, all people who had travelled from Wuhan recently.
A report published by London's Imperial College said there could be as many as 1,723 infections in Wuhan city alone.
“It is likely that the Wuhan outbreak of a novel coronavirus has caused substantially more cases of moderate or severe respiratory illness than currently reported,” said the report.
“Self-sustaining human-to-human transmission should not be ruled out.”
Chinese officials did not immediately respond to requests for comment.
Currently the World Health Organisation and Wuhan health authorities have not concluded that the virus can be passed from person to person.
According to official statistics released on Saturday, 763 people who came in contact with victims were identified by authorities, and 98 remain under observation.
The United States and most Asian countries have stepped up screenings of travellers from Wuhan and the WHO has warned hospitals worldwide that a wider outbreak is possible.
In 2002/03, the SARS virus which originated in China killed nearly 800 people worldwide. People in Wuhan who spoke to Reuters said that while many are reviewing travel plans as a precaution, general anxiety over the virus is low.
Businesses are operating normally in the city, which has a population of over 8 million, they said.
More than 400 million Chinese people, mostly migrant workers returning to their home towns, are expected to make 3 billion trips over the new year beginning on January 24.
A person who works for China's official train ticketing service told Reuters on Friday that there were no additional health screening measures or temperature checks in place at Wuhan train stations.
Since Wednesday, people travelling from Wuhan's Tianhe International airport have been subject to temperature tests before boarding flights, according to an official notice.
Two flight attendants staffing separate domestic flights in and out of the city said they had not received additional training or warnings about the virus.
But people who have been affected are worried.
“I look at a public handrail or food or people standing close together and it makes me feel anxious,” said a 33-year-old woman surnamed Peng, who lives roughly one km (a half-mile) from the seafood market where the virus is suspected to have originated and says her elderly aunt was hospitalised with flu-like symptoms late last week.
As the number of new cases continues to rise, locals say authorities are cracking down on people who post online information on the virus or sick relatives.
Earlier this month, State media said eight people had been ”dealt with according to law” in cases related to sharing information about the virus on social media.
Two people told Reuters they had been ordered by police to remove social media posts. They declined to share their names.
Several source said admittance departments at hospitals in Wuhan were unusually busy and many people with flu symptoms were told to return home.
“People are scared,” said Peng. “Most people maybe have a regular flu or cold but where is the person who takes that chance?”
