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The Tokyo Olympics have ended, but it’s still vacation season in Japan, and many people are ignoring government pleas to avoid travel and stay away from bars and restaurants even as the coronavirus spikes at record levels.

Prime Minister Yoshihide Suga is pinning his hopes on vaccinations, which started slow but now are making good progress. How this race between shots and disease finishes may determine Suga’s political future, not to mention the health of tens of thousands.

Suga seems optimistic vaccines will win, but with only about 36% of the population fully vaccinated, experts say the virus’s highly infectious delta variant is pulling ahead. They are urging the government to put more teeth in its weak state of emergency. Japan has managed the COVID-19 pandemic better than many countries, without the kind of restrictive lockdown used in other nations, but some believe that may now be needed.

Japan’s daily coronavirus cases have topped 10,000 for more than a week, and the total has doubled in the past four months to exceed 1 million. Tokyo’s daily caseloads tripled during the Games that ended Sunday. And as hospitals fill up, nearly 18,000 infected people are isolating at home, over 10 times more than a month ago.

Suga has stressed the progress of the vaccine rollout despite its late and slow start.

More than 80% of Japan’s elderly population of 36 million have completed their vaccinations since they started getting shots in mid-April. Suga says high inoculation rates among seniors have contributed to a significant decline in the number of elderly patients, serious cases and deaths, relieving strain on the medical system.

“This clearly shows the vaccine efficacy,” Suga said, pledging to accelerate vaccinations among younger people. “The most effective way to slow the infections and minimize serious symptoms would be to give everyone two shots as soon as possible.”

Serious cases are now mostly among people in their 50s or younger, who are still largely unvaccinated. So far, 14 million — less than 20% of those aged 12 to 64 who are eligible for shots — have been fully vaccinated, according to Taro Kono, the minister in charge of vaccinations.

Suga said his goal of fully vaccinating all willing elderly people by the end of July has been mostly achieved. As he pushes to inoculate younger people, Suga aims to fully vaccinate 40% of all those 12 years and older by the end of August, and to complete shots for all those who wish to do so by October or November.

But vaccines alone might not be enough, experts and officials say.

“With the ongoing surge accelerated by the delta strain, it is extremely difficult to deal with the infections just by promoting the vaccines,” Kono told a recent online program. He noted that young adults in their 20s and 30s account for about half of daily cases and urged them to stick to social distancing, mask wearing and handwashing.

Japan’s delayed vaccinations began in mid-February, with medical workers getting the first shots. The pace, initially slowed by logistical bungling, inefficiency and shortages of vaccine supplies, dramatically picked up in May, and the number of daily shots has since risen beyond 1 million, meeting Suga’s ambitious target.

Officials expect the vaccination pace will slow when young adults get their turn because of their reluctance to get jabs, in part because of false rumors about side effects. Many of them also think they are less likely to develop serious symptoms.

For Suga, who has been criticized for forcing through the Games despite strong local opposition, showcasing the relative safety of the Olympics and Japan’s vaccination progress may be key to his political survival. Suga has repeatedly said there is no evidence of the virus spreading from the Olympics, and organizing officials agree. While some 400 positive cases were reported inside the Olympic “bubble” from early July until the closing ceremony, that positivity rate is only a fraction of Tokyo’s overall, they say.

Suga said his government is urgently tackling the surge of infections, but his government has repeated the same set of unpopular emergency measures that mainly target bars and restaurants, requiring them not to serve alcohol and close early. Department stores, entertainment facilities and other non-essential businesses are also requested to close at 8 p.m.

Though businesses that comply receive a daily compensation of up to 200,000 yen ($1,800) and those that defy could be fined, thousands are staying open later than 8 p.m. The authorities can stiffen the requests to orders and eventually impose fines on those who defy, but punishment is rare amid growing criticism that the measures unfairly target eateries.

Measures aimed at the public, including masking, disinfecting and avoiding non-essential trips, are only requests, and many people still roam around, go to restaurants, gather in parks and streets to drink and commute on packed trains.

Economy Revitalization Minister Yasutoshi Nishimura, also in charge of virus measures, noted this week that large infection clusters have been detected in classrooms, department stores and “pachinko” pinball parlors, and asked that people avoid traveling during the summer vacation season.

Despite increased support for the Games thanks to a record 58 Japanese medals, post-Olympic media surveys show support ratings for Suga’s government dropped below 30%.

“The government should come up with measures on the premise that people won’t listen to its requests,” former Osaka governor and political critic Toru Hashimoto said on a television talk show this week. “Many people think it doesn’t make sense that only they have to keep restraining their activity even though the government forced through the Olympics.”

The state of emergency is no longer working, some say, because measures have dragged on and people are tired of following the government requests.

“If the infections continue to escalate, we may have to start discussing the possibility of legalizing a lockdown,” said Dr. Shigeru Omi, the government’s top medical adviser. “Political leaders did not send a unified, powerful and clear message” to persuade the public to cooperate in order to slow the virus’ spread.