Kaiser Permanente, one of the nation’s largest nonprofit health plans, announced its vaccination requirement on Aug. 2, when 78 percent of its work force had already been inoculated. A spokesman said this week that the level had risen to more than 92 percent.

Still, about 1 percent of Kaiser’s work force across the country — approximately 2,200 workers — were put on unpaid administrative leave because they had not met the requirement, the spokesman said. They have until Dec. 1 to get vaccinated to be able to return to work.

The Henry Ford Health System required its employees to comply with a vaccination requirement by last Friday. The system said on Tuesday that 99 percent of its 33,000 employees had been fully vaccinated, were soon to get their second dose or had received medical or religious exemptions.