As the second wave of Covid-19 patients fills hospitals across Europe, countries that managed to keep case numbers and deaths low in the initial wave are introducing further lockdowns, extending online learning and preparing their health care systems as they try to stave off rising infection rates.

Bulgaria has seen the number of people per 100,000 hospitalized with the virus more than triple compared with the spring outbreak. Prime Minister Boyko Borissov is among those who caught the virus in the second wave.

The country has made wearing face masks obligatory in all outdoor spaces until the end of the month and many school students who have been learning from home have been instructed to continue with online classes for at least a few more weeks.

An 11 p.m. curfew was introduced in Bosnia and Herzegovina on Wednesday. The nation has seen an average of 1,566 daily cases in the past week, according to a New York Times database.

Lithuania, already in a three-week national lockdown to stem the spread of the virus, has seen the number of daily cases increase tenfold from a month ago. Officials in the capital, Vilnius, are preparing a makeshift hospital that can accommodate up to 700 patients in an exhibition center after fears the number of people requiring medical treatment could soon overrun the city’s hospitals.

In other news from around the globe:

Athletes traveling to Japan for the Tokyo Olympics next summer will not be subject to the 14-day quarantine requirement, organizers said Thursday, though they must test negative before and in some cases after they arrive. Rules have not yet been decided for spectators at the Games, which were postponed for a year because of the pandemic.

All kindergartens and day care centers in Hong Kong will close for two weeks as a precaution, health officials said on Thursday, citing a cluster of more than 100 upper respiratory tract infections. So far, no students or teachers have tested positive for the coronavirus, but some have symptoms that are associated with it. Day care centers and kindergartens reopened in late September after spending most of the year operating remotely.

President Volodymyr Zelensky of Ukraine was hospitalized after he contracted the coronavirus this week, a presidential official said on Thursday. He moved to the hospital to “accurately isolate and not expose anyone,” a presidential spokeswoman told Reuters. “There are better conditions for patients. Nothing serious,” she said referring to the president’s health. Mr. Zelensky said on Monday that he had tested positive for coronavirus. Three other top officials, including the finance minister, the defense minister and Mr. Zelensky’s top aide, were also reported to be infected.

As cases continue to grow in most of Canada, the western province of Manitoba implemented sweeping restrictions on Thursday. The orders closed most stores other than grocers and pharmacies, sports fields and playgrounds, bars, cinemas and theaters. Restaurants are limited to takeout service and a maximum of only five people may gather indoors or out. Manitoba’s cumulative number of cases reached a record 9,308 on Wednesday, up from 1,232 at the beginning of September.

Almost two weeks into a second national lockdown, a surge of coronavirus cases in France appears to be slowing. France has reported an average of 25,000 new Covid-19 cases per day since the beginning of the week, which is about half as many as last week. Meanwhile, the reproduction rate — which refers to the number of people an infected person contaminates — has fallen below one, according to health authorities. Still, more than half of French people surveyed said they have broken the rules of the lockdown at least once, according to IFOP, an international polling firm.

The European Union has increased its support for COVAX, a global fund that aims to ensure that low- and middle-income countries have access to a Covid-19 vaccine. The bloc’s total contribution is 500 million euros. As of now, 184 countries — 92 of them low- and middle-income economies — participate in COVAX, whose goal is to procure 2 billion doses of a vaccine by the end of 2021. Vaccines would be delivered by UNICEF and the Pan-American Health Organization.

— Anna Schaverien The New York Times