Medicines exist to stop the AIDS epidemic right now, but access to health care and stigma surrounding the disease remain critical barriers, the NIH’s infectious disease chief said.

“If you could treat everyone in the world that’s infected with HIV you could stop the epidemic tomorrow,” Anthony S. Fauci, director of the National Institute of Allergy and Infectious Diseases, part of the National Institutes of Health, said July 18.

More than 70 million people have been infected with HIV since the 1980s, resulting in 35 million deaths and more than 36 million people currently living with the virus worldwide, Fauci...