The rapid spread of the delta variant of the coronavirus is poised to divide the United States again, with highly vaccinated areas continuing toward post-pandemic freedom and poorly vaccinated regions threatened by greater caseloads and hospitalizations, health officials warned this week. The highly transmissible variant is taxing hospitals in a rural, lightly vaccinated part of Missouri, and caseloads and hospitalizations are on the rise in states such as Arkansas, Nevada and Utah, where less than 50 percent of the eligible population has received at least one dose of vaccine, according to data compiled by The Washington Post.

One influential model, produced by the Institute for Health Metrics and Evaluation at the University of Washington, predicts a modest overall surge in cases, hospitalizations and deaths this fall. Scott Gottlieb, a former head of the Food and Drug Administration, said Sunday that a fall surge could occur even if 75 percent of the eligible population is vaccinated.

“I think a rise in cases is certainly going to happen,” said William Hanage, an associate professor of epidemiology at the Harvard T.H. Chan School of Public Health. The question “is how large a rise and how consequential it’s going to be.”

“Those under-vaccinated communities are more likely to be severely” affected, he said.

At a briefing by the White House Covid-19 Response Team on Tuesday, Anthony S. Fauci, the nation’s top infectious-disease specialist, said “there is a danger — a real danger — that if there is a persistence of a recalcitrance to getting vaccinated, that you could see localized surges, which is the reason why I want to emphasize what all four of us have said: All of that is totally and completely avoidable by getting vaccinated.”

In general, rural and Republican areas have embraced vaccination less than cities and Democratic states in the Northeast and along the West Coast. All of the states in New England have given at least one dose to 61 percent of their residents or more. In San Francisco, 65 percent of residents are fully vaccinated.

Overall, the nation has made significant progress against the virus. The seven-day average of new daily cases has plummeted to 10,350, and deaths are down to an average of 273 each day, Rochelle Walensky, director of the Centers for Disease Control and Prevention, reported Tuesday. Those figures are a small fraction of average daily peaks of nearly 250,000 cases and 3,300 deaths in January.

In addition, with 80 percent of adults older than 65 vaccinated, the most vulnerable population is largely protected. That should mean many fewer deaths and hospitalizations even if another widespread surge were to occur this fall or winter.