LOS ANGELES—Los Angeles County health officials have asked federal officials for help to contain a worsening tuberculosis outbreak among the homeless in its downtown area.

County health officials here have identified 78 cases of a particular strain of the highly contagious disease in the past five years, resulting in 11 deaths. Of those cases, 60 have been identified as homeless living around Skid Row, making it the "largest outbreak we've seen" among the city's homeless population in a decade, said Dr. Jonathan Fielding,...