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L.A. begins a testing program expected to be among the most comprehensive U.S. school-based initiatives.

A sweeping initiative to test and screen all 700,000 students and 75,000 employees in the Los Angeles public schools for the virus has started, with five cases last week among more than 5,400 children and adults tested, the district’s superintendent said.

All were among adults who work for the district. Up to 20,000 more employees are to be tested this week, said Austin Beutner, the superintendent, whose Los Angeles Unified School District is the nation’s second largest, behind New York City’s.

Some 700 small children in district-provided child care were also tested, said Mr. Beutner, but none were infected.

With the exception of certain special-needs students, who recently got the go-ahead to return to classrooms for very limited instruction, classes at Los Angeles Unified have been remote.