Some speakers defined an AIDS-free generation as the absence of people sick from the disease. But even if there is no one with AIDS, there will still be millions of H.I.V.-infected people with us for a very long time. In those terms, H.I.V. will likely be endemic until there is a cure.

Dr. Helen Rees, an AIDS expert at the University of the Witwatersrand in Johannesburg, said that while scientific advances provide “cause for optimism,” the fact is that if many infected people stop taking their drugs, even for brief periods, they could transmit H.I.V. to others - and those strains may well be drug-resistant.

This is not the end of an epidemic in any sense as we have understood it; an AIDS-free generation, if it arrives, will live in a world where H.I.V. very much remains a threat. Dr. Peter Piot, the United Nations AIDS program’s first director, from 1995 through 2008, said in an interview that he was “puzzled” by the apparent lack of attention to such distinctions at the conference.

“Which generation?” asked Dr. Piot, who is now the dean of the London School of Hygiene and Tropical Medicine in England. “Mine? Or the next one? Or my great-grandchildren’s?”

Bill Gates, whose foundation is spending billions on developing AIDS preventions, expressed skepticism that the world could soon end the AIDS epidemic by any conventional definition. “Unfortunately, we do not have the tools, and we need lots of new tools,” with a vaccine the ultimate preventive one, Mr. Gates told the conference.

He and others called for greater accountability from AIDS workers in identifying the measures that work so they can be stepped up and those that do not so they can be stopped. For example, in countries where young people are dying in excessive numbers, he said, health workers must learn “why they did not start treatment, and if they were on treatment, why did it not work?”

The AIDS epidemic is not unfolding uniformly across the globe. Speakers cited an undertaker in Lesotho who said he was going out of business because of poor coffin sales, as so many people with H.I.V. are staying alive.

But undertakers do a brisk business in other countries with a rising AIDS incidence. In some ways, this is not just one epidemic. Scientists often use the term “R0” as a statistical way to monitor an epidemic, with “R” standing for the reproductive number of an infectious disease agent.

When, on average, one infected person transmits an infection to more than one other person, R0 becomes greater than one, leading to sustained spread or epidemic spread of the agent. When R0 is less than one, epidemic spread does not occur, and the agent will become endemic or disappear.

In AIDS, R0 depends on a number of factors, like the prevalence of H.I.V. in a sexual network and the efficiency of H.I.V. transmission per sexual act. The R0 varies in the many different H.I.V. epidemics in the world.