President Trump’s 2020 budget request of an extra $291 million to fight the spread of H.I.V., experts said on Tuesday, will not be remotely sufficient to meet the goal he announced in his State of the Union address: to nearly eliminate the AIDS epidemic in the United States within 10 years.

Mr. Trump’s plan focuses on 48 counties where about half of new infections occur, and seeks to cut the rate of new infections by 90 percent — from about 40,000 a year to about 4,000.

Virtually all H.I.V. experts agree that his plan is medically sound. People living with H.I.V. cannot transmit the virus if they are taking a daily triple-therapy drug cocktail. And a two-drug regimen, in a single daily pill known as PrEP, makes it almost impossible to get H.I.V., even through unprotected sex or needle use.

But the plan requires a vast two-pronged attack. All Americans with H.I.V. must be found, put on antiretroviral drugs and kept on them for life; and all those at high risk of infection must be put on PrEP for as many years as they are sexually active or using drugs.