Hong Kong (CNN) Weeks into the novel coronavirus crisis , the outbreak finally appears to be stabilizing in central China, where the virus was initially detected before it spread throughout the country and the world.

Small outbreaks continue to fast expand elsewhere, however, not least of which on board the Diamond Princess cruise liner in Japan, where two deaths were confirmed Thursday, the first from the hundreds of cases on the ship, which has begun disembarking passengers after a 14-day quarantine this week.

The global death toll now stands at 2,129, after an additional 108 deaths were reported in Hubei province as of Thursday morning. All but 11 deaths have occurred in mainland China. On Thursday, South Korea reported its first death from the virus.

An additional 349 cases were confirmed in Hubei, more than 1,300 fewer than reported the day before. Outside of the provincial capital Wuhan, epicenter of the outbreak, the daily count of patients who have been treated and discharged has exceeded the number of newly confirmed cases for four consecutive days now, according to state news agency Xinhua

There is some uncertainty of how cases are being diagnosed in Hubei, with the criteria for diagnosing the virus outside of the lab shifting in recent weeks. Chinese authorities this week switched back to reporting only laboratory confirmed cases from Hubei, after last week allowing clinical diagnoses by doctors -- based on symptoms or more immediate tests -- to be counted towards the province's totals.

More than 10,330 patients have been discharged across Hubei so far, though some 43,000 remain in hospital, 2,050 of whom are in a critical condition, the provincial health authority said.

The Chinese Center for Disease Control (CCDC) previously estimated that the virus peaked in late January, according to data from lab tests. However, the number of clinically diagnosed cases -- patients with symptoms who could not be tested or were believed to have falsely tested negative -- continued to rise well into February.

While the data from the epicenter of the outbreak appears to be positive, the crisis may not be over yet, either inside China or worldwide. Experts have warned there could be a renewed increase in cases once China properly returns to work late this week or next -- hundreds of millions of people around the country have been on lockdown for weeks now.

The number of cases is also continuing to grow alarmingly in several places outside of the mainland, though still far short of the figures seen in China. On Thursday, South Korea recorded an additional 31 confirmed cases, bringing the country's total to 82. That came after an increase of 20 on Wednesday, previously the largest single-day jump in Korea.

In Singapore the infection rate continues to climb, with 84 confirmed cases. Similarly, in Hong Kong, there are 63 confirmed cases, and two deaths.

In Japan, where global attention has been focused on the Diamond Princess cruise liner, the worst outbreak outside of mainland China, there have been 68 cases confirmed with no connection to the ship, raising concerns of a self-sustaining outbreak in the country.

Cruise ship disembarks

More passengers from the Diamond Princess disembarked Thursday morning , though serious questions remain over the effectiveness of the two-week quarantine imposed on the ship since it first docked at the Japanese port of Yokohama.

When the first load of passengers left the ship over the weekend, on a pair of flights to the US, more than a dozen of the 300 or so on board were found to be showing symptoms of the virus . All of those who had boarded the planes were supposedly coronavirus free, according to Japanese authorities.

The Japanese quarantine officially ended Wednesday, and the first group of passengers began disembarking. Hundreds of cases have been confirmed on board, however, and on Thursday authorities in Japan confirmed the first two deaths from Covid-19, the disease caused by the coronavirus.

Jan Swartz, President and CEO of the vessel's operator Princess Cruises, who had flown to Japan to greet the passengers as they left the ship, said that those on board united to help each through an "unprecedented situation."

"I think the guests and our crew who came together to help support each other, from 57 different countries and regions around the world, really lifted each other's hearts," Swartz said.

Multiple countries have arranged flights to bring their citizens home once they disembark -- so long as they do not test positive for the virus. Canada has chartered a plane from Tokyo's Haneda airport Friday. The 47 Canadians who had been found to have the virus would receive medical care in Japan, the government said in a statement.

The early evacuation of Americans from the ship was seen as something of an implicit criticism of the Japanese quarantine, with the Centers for Disease Control saying that remaining on the ship was an ongoing risk to US citizens.

Speaking to CNN this week, Kentaro Iwata, an infectious disease specialist at Kobe University who visited the ship, said he was highly concerned about the effectiveness of the quarantine and the precautions taken on board.

"I was so scared because there was no way to tell where the virus is and everybody was not careful about it," Iwata said. "There was no single infection control person inside the ship -- the bureaucrats were in charge of everything."

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Economic woes

Japan is likely facing a recession as the coronavirus compounds existing problems with the country's economy. In China, while the worst of the virus is hopefully past, the economic cost has yet to be fully realized, and there are fears it could continue to grow and have knock-on ramifications for the global economy.

China's central bank promised more support Wednesday for companies, including lowering lending rates, increased credit support and providing medium and long-term loans. The People's Bank of China said the epidemic "has had some impact on the Chinese economy, but the shock will be short-lived and will not change the country's sound economic fundamentals."

Other outlooks are not so rosy . Around a third of 1,000 small and medium-sized companies surveyed by academics from Tsinghua University and Peking University last week said they could only survive for a month with the cash they have.

Smaller companies account for around 60% of China's GDP, and employ a massive 80% of all workers, according to government statistics published last September.

"The coronavirus could be the straw that breaks the camel's back," wrote Zhao Jian, director of the Shandong province-based Atlantis Research Institute in a research note earlier this month.

He warned that if the outbreak doesn't end soon, unemployment will likely rise as businesses shut down -- a problem Beijing had been fighting hard this year to prevent. Job losses could spur a tide of housing foreclosures, Zhao added, compounding the country's economic woes.

Even as the country starts to get back to work, problems remain for smaller firms. According to the state-backed Global Times , Chinese factories and businesses trying to resume operations this week have been "faced with tremendous risks and challenges, from lengthy applications to tough restrictions and shortages in cash, labor and supplies."

Companies have reported having to submit up to 21 separate documents, including a 15-page application form, emergency plans and various other letters of commitment, to local officials. A screenshot of an application from a company in Sichuan province went viral on social media this week -- a single application to resume operation require a total of nine stamps from various county and provincial officials.

"These are the unintended consequences of the battle against the epidemic: the restrictive measures put in place to stop the virus have also restricted companies from resuming production," Tian Yun, director of the China Society of Macroeconomics Research Center, told the Global Times. "In some places, officials have taken the battle to a whole new, unnecessary level."