The Cambridge Housing Authority has begun requiring employees who work in person to test themselves for coronavirus just before they start work, and it may have paid big dividends in preventing transmission of the virus. The requirement relies on employer-provided rapid antigen tests.

Despite what Cambridge’s chief public health officer called “uncontrolled transmission” of Covid-19, the city won’t require restaurants, fitness centers and other indoor public spaces to mandate Covid-19 vaccination for their customers and workers, as Boston and neighboring communities have done.

Cambridge city workers don’t have to get vaccinated against Covid-19 to keep their jobs, but the city will make it easier for them to get a shot if they want one. The city plans three vaccination clinics specifically for Cambridge employees and their families this week.

About 72 percent of fully vaccinated Cambridge residents 65 and older have received a third shot, according figures reported by the city for the first time Thursday, as 391 new cases of Covid were reported. The cases strained hospitals, nursing homes and even a library branch that will be closed for nearly a week.

Cambridge reported 324 cases of Covid-19 on Thursday and two deaths, the first increase in deaths since Nov. 3 and a sign that the record-breaking increases in cases are having a grim impact. The city has been offering free testing four days a week but will go to seven days a week starting Monday and lasting the month of January.

Almost all staff who care for vulnerable residents at Cambridge’s three nursing homes are fully vaccinated against coronavirus, but less than one-third of eligible employees have received a booster shot in two facilities.

Cambridge reached a milestone of sorts on Thursday: The city has now recorded more than 10,000 cases of Covid-19 among its residents since early March 2020. The Cambridge Public Health Department reported 220 new infections on Thursday – another daily record – to bring the total to 10,141 cases.

Cambridge’s two hospitals, Mount Auburn Hospital and CHA Cambridge Hospital, are full as Covid-19 case counts and hospitalizations in Massachusetts grow. Gov. Charlie Baker on Tuesday ordered hospitals to postpone all elective procedures likely to result in hospital admissions.

Racing to deal with exploding Covid-19 infections, Cambridge is distributing 46,000 free Covid-19 rapid antigen test kits to organizations serving low-income residents, hoping to get the tests out before Christmas and New Year’s Eve gatherings.

The city reported a record 143 new Covid-19 cases Thursday, the highest one-day increase since the pandemic began in March 2020. The Cambridge Public Health Department said 53 percent of new cases in the two days on Wednesday and Thursday were residents in their 20s; another 16 percent were people younger than 20.