WASHINGTON—Federal agencies are preparing to deploy emergency plans to maintain essential services—from directing air traffic to delivering mail and making Social Security payments—as the novel coronavirus epidemic widened and the nation’s capital diagnosed its first case.

Some agencies are canceling nonessential travel. All are planning for widespread absences and making provisions for working remotely. Some workers, like food-safety inspectors, won’t have that option; the challenge will be keeping them safe and healthy.

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