DAVEYTON, South Africa — South Africa, already home to 5.7 million H.I.V.-positive people, more than any other nation, can expect an additional five million to become infected during the next two decades even if the nation more than doubles its already considerable financing for treatment and prevention and gives prevention a higher priority, according to a report presented here Friday to the country’s leading advisory body on AIDS policy.

South Africa has far and away the continent’s leading economy, but the study concludes that it nevertheless faces a “major and mounting financial challenge” to confront its AIDS problem, explaining that about $102 billion will need to be spent over the next 20 years merely to keep the number of new infections at the projected five million mark.

“The government doesn’t seem to have their heads around the numbers yet, and they are going to have to do some thinking out of the box,” Teresa Guthrie, an economist and one of the report’s authors, said in an interview. “It’s not an encouraging picture.”

Actually, South Africa is in the midst of a rapid expansion of its AIDS programs, attempting to overcome years of denial and delay when former President Thabo Mbeki questioned whether H.I.V. caused AIDS. He suggested that antiretroviral drugs were harmful, and his health minister recommended remedies of beet root and garlic.

Last year, the nation spent $2.1 billion on AIDS, according to the report, though about a third of that came from international donors, including $620 million from the United States.

“We would argue that the donors really need to stay with this, and the next five years are absolutely critical,” said Robert Hecht, another of the report’s authors.

The government itself requested the study, which is called “The Long-Run Costs and Financing of H.I.V./AIDS in South Africa.” It was done by the Center for Economic Governance and AIDS in Africa, based in Cape Town, and the Results for Development Institute, based in Washington.

Mr. Hecht, a managing director of the institute, presented the findings at a meeting of the South African National AIDS Council, a group that includes leaders from both the government and civil society.

None of the government officials at the meeting were willing to comment on the report, but Mark Heywood, the council’s deputy chairman and executive director of the AIDS Law Project, which is based in Johannesburg, said later that he was “gravely concerned” about the numbers cited.

“I found it all difficult to accept,” he said. “Our prevention strategy was such a mess for such a long time that I felt sure we could bring down infection rates at a faster pace now that we’re working at it.”

Mr. Heywood said he did not know where any extra financing would come from. “I think the budget is strained already,” he said.

In the past year, the government has widely increased treatment with antiretroviral drugs and begun a campaign for counseling and testing. The report said it needed to go much further, emphasizing male circumcision, which has been shown to decrease by more than 50 percent the rate of contracting H.I.V., and the promotion of condom use.

“Things are still not being done fast enough and broadly enough,” Mr. Hecht said. “The big, looming, difficult problem to crack is the general adult population and the millions of people with multiple partners and overlapping relationships. That’s the big challenge for South Africa.”

In South Africa, with a population of 49 million, an estimated 350,000 to 500,000 new infections occur annually, depending on the estimate. With enough money and better programs, that number could gradually be brought down to 200,000 a year, Mr. Hecht said. This can be accomplished, the report said, by 2020.