In the past, global health officials have treated the epidemic as a cyclone spiraling ever upward with no end to new infections in sight.

But better surveys, particularly a household survey in India, have driven the figures down.

Until recently, most national estimates were made by giving anonymous blood tests to some young women who came into public health clinics because they were pregnant or feared they had a sexually transmitted disease; those results were expanded with statistical models.

But epidemiologists have realized that such a method — usually applied in big urban clinics because it was more efficient — oversampled prostitutes, drug abusers and people with multiple partners, and ignored rural women. Then the statistical extrapolations exaggerated those errors.

Recently, the United States Agency for International Development began financing surveys that chose thousands of households at random in both urban and rural areas and sent in health care workers to take detailed medical and lifestyle histories and blood samples; though expensive, they produced results that are considered more accurate.

In July, India’s estimated caseload was revised downward, to 2.5 million, from 5.7 million — a change that accounts for about half the drop in the new Unaids figures. Officials said then that India’s epidemic was not “generalized” — that is, it had not spread far from the original high-risk groups like brothel workers and clients, truckers, heroin users and gay men. Also, rates among prostitutes appeared to have fallen as condoms gained acceptance. Instead of being considered the world’s worst-hit country, India fell to third place behind South Africa and Nigeria.

Also, some African countries have seen real drops in new cases. It happened relatively early in Uganda, after an aggressive “no grazing” (meaning no casual sex) campaign started 20 years ago. Similar declines appear to have happened in Zimbabwe and Kenya, especially since people saw many friends and relatives die. Rather than embracing condoms, people decided to have sexual relations with fewer people, Dr. Halperin said.

“You don’t need a Ph.D. to figure out that if you reduce your number of partners, you reduce your risk,” he added.