The rules for patients don’t always accord with the science, said one nurse at Rhode Island Hospital. At first, the hospital did not allow anybody up from the E.R. until test results were back. But as the first surge ebbed, the rules became lax.

Patients were sent up with pending test results, potentially exposing other patients as well as the nurses who cared for them. After treating one such patient, at least nine nurses tested positive for the virus, the nurse said.

The policy at most hospitals in Rhode Island now is to have health care workers wear N95 respirators or similar reusable masks at all times, and to test anyone suspected of having Covid-19. But that does not account for patients who might be asymptomatic and who come in for other ailments.

Rhode Island has adopted one unusual approach: Officials are distributing vaccines to anyone who will take them in Central Falls, regardless of age. It’s a strategy that few other jurisdictions have tried.

“We decided to do that because of the horrific toll of the pandemic in those communities,” said Dr. Rodriguez, the vaccine committee member. Twenty percent of the adult residents have received at least one dose at local clinics, not including those who may have been immunized at work or elsewhere.

The state’s plan to immunize those at highest risk by age and geography, he added, “will put out the fire where it is burning the most intensely.”

In recent weeks, the number of cases in Rhode Island have fallen, as they have in the rest of the country. And fewer health care workers are getting sick because they have been immunized, so hospital shifts are better than they used to be, Dr. Ranney said.

But cases in the state are still the third highest per capita in the country. And doctors are continuing to see patients who have so-called long Covid, she said: “The trouble is that once patients get admitted, they don’t leave.”