Dr. Timothy Farrell, a geriatrician at the University of Utah, said he was surprised but thrilled by the vaccines’ effectiveness in this group. “It’s going to be very important to see the subgroup analysis,” he said — that is, to learn whether there are significant differences after age 85.

Even so, he has been recommending the vaccine to all of his patients, who range in age from 65 to 106 years old.

“We have a clear and present danger of Covid, and we have social isolation,” Dr. Farrell said. “We know that that’s an independent risk factor for mortality, even stronger than individual chronic diseases.”

Dr. Inouye also arrived at the same conclusion, both professionally and personally.

Her 91-year-old mother, who lives in an assisted living facility, is independent and spry, still playing piano and bridge and exercising regularly. Still, her mother’s age, medical condition and living situation put her at “very, very, very high risk for Covid,” Dr. Inouye said.

“We’re just desperately worried about her every single day,” she added. “When you balance that tremendous fear, I just think the risk for her of getting Covid is so much higher than the risk of a side effect, which we know is going to be very rare.”

For many people, the prospect of receiving a new vaccine for a new virus is daunting.

Fear of side effects deterred Jeffrey Balkind’s wife from volunteering for the vaccine trials, but Mr. Balkind, 74, has stared down death twice — once during a 13-day hijacking in Pakistan in 1981, and again three years ago when his Vespa crashed.

“When you’ve come to near-death experiences twice, volunteering for a vaccine trial — it wasn’t a great sense of worry or apprehension for me,” Mr. Balkind said.