With the number of COVID-19 cases in Tokyo having nearly quadrupled in 10 days, it seems no longer a question of whether Japan will declare a national emergency, but when and how.

Officials and experts fear the capital city may not be prepared to handle an explosive rise in the number of cases that would overwhelm hospitals and collapse the health care system, also described as an “overshoot.”

Though officials maintain that an overshoot has not yet occurred in Tokyo, or anywhere else in the country, they say the danger remains imminent.

“In many ways, hospitals in Tokyo are not prepared for that situation,” said Koji Wada, a professor in public health at the International University of Health and Welfare and a member of the government’s expert panel on COVID-19.

As it stands, Tokyo has designated mostly publicly funded hospitals to take in coronavirus patients. But those facilities are starting to show signs of exhaustion, Wada said, and won’t be able to handle a significant increase in patients.

As of Monday, the Tokyo Metropolitan Government said it had 500 hospital beds in total for COVID-19 patients, and that 394 were occupied. Aware of the risks that poses, the city aims to obtain 700 additional beds for patients experiencing severe symptoms and 3,300 for less severe cases.

The health ministry has estimated that Tokyo could see up to 530 cases in total before April 8 if stricter measures are not taken. And when the pandemic peaks, the city may have to deal with up to 700 new patients in need of intensive care daily as well as more than 20,000 requiring treatment for pneumonia.

To avoid a collapse of the capital’s health care system — a grim scenario in which otherwise treatable patients would lose their lives — Wada said financial incentives would be needed to encourage private hospitals and nondesignated medical facilities to take in COVID-19 patients.

Another concern is that the daily reports of newly confirmed cases do not reflect how fast the virus is currently spreading, but rather, how much it has already spread.

As of Wednesday evening, the Tokyo Metropolitan Government had reported 521 cases of the novel coronavirus and 16 deaths. As many as 78 cases had been reported the previous night, following a turbulent period in which seven record-breaking days brought the tally in the capital to the highest among all 47 of the nation’s prefectures. Tokyo was slated to announce up to 66 additional cases Wednesday night, bringing the tally in the capital close to 600.

For most patients, two to three weeks have elapsed since they were infected by the time they test positive and the case is made public. It’s also possible to carry the virus for up to two weeks before developing symptoms.

What that means is that many of the numerous cases reported in Tokyo over the past week reflect infections that took place weeks ago. New cases, of patients infected before the governor began asking residents to isolate themselves, are likely to emerge in the coming days.

The most crucial factor is whether Tokyo has the capacity to treat all patients in need of immediate medical attention.

According to the World Health Organization, 80 percent of COVID-19 patients recover completely after experiencing minor symptoms, while about 15 percent are hospitalized and the remaining 5 percent require intensive care.

In Japan, a small fraction of those intensive care patients are treated using extracorporeal membrane oxygenation, or ECMO, which provides respiratory support with cutting-edge technology and is used occasionally to remedy serious lung problems, as well as heart issues.

There are just over 1,400 ECMO machines in Japan, according to a joint survey released in March by the Japanese Society of Respiratory Care Medicine and the Japan Association of Clinical Engineers. But only about 300 of these machines are available for COVID-19 treatment, said Satoru Hashimoto, the director of intensive care medicine at Kyoto Prefectural University of Medicine’s hospital.

In Tokyo, 16 people among the 521 cases reported so far are suffering from severe symptoms. The city has limited ventilators and fewer than 200 ECMO machines, according to the March survey, only a fraction of which can currently be used for COVID-19 treatment.

To prevent an overshoot scenario from happening, experts say political leaders need to better convey the urgency of the situation so that the public clearly understands the risks at hand. One way to do that would be for Prime Minister Shinzo Abe to declare a state of emergency.

Calls are growing for Abe to make the declaration — an unprecedented move that would endow prefectural governors with greater legal authority in getting residents to isolate themselves.

Municipal governors have the authority to close office buildings, parks and other facilities, but cannot compel residents to stay indoors or punish those who fail to comply. The declaration of a national emergency — which became possible after the central government established a special task force last week — wouldn’t necessarily expand governors’ reach, but it could give them greater authority when communicating their concerns to the general public.

Governors could also call on big companies and transit operators to temporarily shut down. Though the economic fallout would be immense, companies are likely to comply given the gravity of the situation.

Tokyo Gov. Yuriko Koike was trying to convey such a message and prevent a disaster when she urged residents to stay inside last week, work remotely if possible and avoid nonessential outings over the weekend. She added on Monday that similar precautions should be taken throughout the week as well.

In particular, Koike has said that if an explosive rise in cases were to occur in Tokyo, “the city’s hospitals would be overwhelmed and the lives of residents could be put in serious danger.”

Her call for residents to isolate themselves over the weekend seems to have been heard, said Kenneth McElwain, a professor who specializes in public opinion at the University of Tokyo’s Institute of Social Science.

But people are still resistant to behavioral change, he added, thanks to the weak messaging and repetitive rhetoric being used by Koike, Abe and other Japanese political leaders. That, coupled with low levels of COVID-19 testing in Japan, leaves residents unsure about the true severity of the domestic epidemic.

Whether it was due to the governor’s urging or the inclement weather, the capital was comparatively quiet over the weekend.

East Japan Railway Co. reported a 70 percent drop in traffic, and officials said the Toei Subway System — which is operated by the city — saw a 66 percent decrease on Saturday and Sunday.

Whether the appeal and measures achieved the intended results, however, won’t be seen for another few weeks.

“If the government’s message is that people should carry on or do what they’re doing now, then perhaps the messaging is fine,” McElwain said. “But if the message is meant to be, `You need to be more careful and modify your behavior more,’ then I’m not convinced that the approach being taken by Gov. Koike or the Cabinet is up to snuff.”

RELATED PHOTOS Few could be seen at the normally crowded Shibuya Crossing on Sunday after Tokyo Gov. Yuriko Koike urged people to avoid nonessential travel over the weekend. | RYUSEI TAKAHASHI