Northwell Health, which has cared for thousands of coronavirus patients in its network of facilities in New York State, sent a nurse manager to Ms. Murray’s home in May. Covered head to toe in protective gear — gown, gloves, mask, shield and disposable bootees — she spent nearly eight hours doing an assessment.

Ms. Murray was dehydrated and in need of supplemental oxygen. Within hours, she was hooked up to an intravenous line, set up in her bedroom to replenish her fluids. A phlebotomist in an N95 mask came to draw blood, an oxygen machine was delivered to her home, and Ms. Murray was prescribed a powerful blood thinner to prevent clots…

So-called wraparound home care services were created, on the fly, by Northwell Health to deal with the surge in coronavirus cases that New York experienced this spring. Now this model may help relieve health systems in the Sun Belt and other parts of the United States, where rising numbers of cases are putting extraordinary pressure on hospitals, filling intensive care units and sending providers scrambling to hire extra nurses and secure medical supplies.