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Even in places where the number of new cases is beginning to flatten, it is doing so at a very high level: New York, which reported its fewest new cases in a month and its lowest one-day death toll in more than two weeks, still reported 4,726 new cases and 478 new deaths on Monday. And the country has added more than 25,000 new cases a day for the past week.

But in some regions there are signs that things are getting worse, not better.

Massachusetts has seen the outbreak hit particularly hard in recent days. It reported 1,705 new cases on Sunday, bringing its total to 38,077, and 146 new deaths, which brought the death toll to 1,706. “We’re right in the middle of the surge now,” Gov. Charlie Baker, a Republican, said Sunday on CBS’s “Face The Nation.”

Los Angeles County reported 81 deaths on Saturday, its highest one-day death toll.

“In this last week we have doubled the number of deaths that occurred among L.A. County residents,” Barbara Ferrer, the county’s director of public health, said in a statement on Saturday. Fewer deaths were reported Sunday — 24 — but county officials noted that nearly a thousand new cases had been identified in the previous 48 hours.

There have been significant workplace-based clusters in North Dakota, Iowa, Minnesota, South Dakota, Kansas, Tennessee and other states, suggesting that the pandemic is just beginning to sink its teeth into some communities.

And nursing homes and prisons continue to be hot spots.

An outbreak at a correctional facility in Goldsboro, N.C., caused cases to spike in Wayne County. More than half of the inmates at the Neuse Correctional Institution — 458 — have tested positive for the virus, county officials said. There have now been 575 cases in the county and six deaths.

Maryland received thousands of tests from South Korea after the governor and his wife closed a deal with labs.