ENTOTO, Ethiopia—Cast out from her family, Tigist arrived at Ethiopia's Entoto Mountain believing that a spring here welled with holy water that would rid her body of HIV.

Joining 4,000 other squatters seeking the same cure, the young woman reluctantly also started taking antiretroviral pills. Gaining strength, she married an HIV-positive man, Melaku, and started a new life in a mud-and-tarp hut amid eucalyptus forests.

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