A couple of years ago, European researchers began studying more than a thousand couples, gay and straight, in which one member had been infected with H.I.V. and the other hadn’t. These couples weren’t using condoms. But the infected partner was taking antiretrovirals successfully; the virus was suppressed, undetectable in the blood. The researchers published their results in July 2016 in the Journal of the American Medical Association.

Can you guess how many times, over the course of more than a year, an infected partner gave an uninfected partner H.I.V.?

A. 928

B. 0

C. 503

D. 17

The answer is B. Zero. And in that fact lies hope.

How do you stop AIDS? Not just treating H.I.V., but ending the epidemic. Even when there’s no vaccine and no cure.

Part of the answer can be witnessed in a white trailer on the grounds of a polyclinic in Hatcliffe, a dusty town in the northern part of greater Harare, Zimbabwe. Even before the trailer opens each day, the benches outside are full of people waiting for a checkup or a fresh supply of medicine for H.I.V. or the diseases that pounce on weakened immune systems.

Hatcliffe’s clinic, like all public clinics in Harare, charges $5 for visits that don’t involve either H.I.V. or tuberculosis. That may seem like a bargain to Americans. But Zimbabwe is in an economic crisis, making millions of people struggle just to buy their staples of cornmeal, sugar and cooking oil.

The clinic is supposed to offer medicines free, but has run out of many, said Sheila Chiedza, the nurse who runs it. (A doctor visits on Wednesdays.) The clinic must send patients to a pharmacy to purchase what they need. “If we don’t have it here, we are not sure if they can get it,” Chiedza said.

For most Zimbabweans, then, medical care at the public clinic is a financial hardship. But H.I.V. and tuberculosis care are different: Drugs are free, each clinic visit costs just one dollar, and most patients come four times a year.

When I visited in August, the trailer’s back office was crowded with staff members entering data. I asked how well patients did on their AIDS meds. “Ninety percent undetectable,” said a young man who gave his name as Mr Edwards.

This seemed unbelievably high. In the United States, the figure is about 81 percent.

But the clinic may not have been exaggerating. Zimbabwe is one of the world’s worst-governed countries and has suffered a staggering economic decline. But it’s doing right by people with H.I.V. — a lot better than the United States.

Every epidemic has a tipping point. When the transmission rate drops below that point, it begins to recede. For H.I.V., reaching the tipping point requires three things: that 90 percent of people with the virus know they have it, that 90 percent of that group are taking antiretroviral medicines to keep the epidemic in check, and that 90 percent of those taking medicine control the virus to the point where it is undetectable and therefore cannot be transmitted.

So having the world at 90-90-90 is the goal of UNAIDS by 2020. If you reach 90-90-90, you end up with 73 percent of people with H.I.V. being noncontagious. That 73 percent is the tipping point, at which the epidemic starts to burn out.

A large part of this success is due to George W. Bush, whose administration established the President’s Emergency Plan for AIDS Relief, or Pepfar, in 2004. Its impact is now evident in the trailer in the yard of Hatcliffe Polyclinic and just about every such trailer in countries with a large H.I.V. burden.

Of course, Bush’s initiative wasn’t alone. Pepfar programs are dwarfed by the Global Fund to Fight AIDS, Malaria and Tuberculosis, which began working around the world in 2002. Most governments take H.I.V. seriously, and campaigns by a global network of people living with H.I.V. and their supporters achieved those victories.

Pepfar began work in seven African countries in 2004, and also contributed to the Global Fund. Now it works in 22 African countries, along with some in Asia and Latin America.

In the past three and a half years, Pepfar has doubled the number of people for whom it provides treatment. It has added a million children in the past two years. On Tuesday, several organizations are releasing household surveys from two more countries — Lesotho, which is near a tipping point, and Uganda, which has stabilized its epidemic.

“Zimbabwe has made great strides,” said Martha Tholanah, a prominent campaigner there for the rights of H.I.V.-infected and gay people. Everyone I spoke with agrees.

This is all the more remarkable given the economic catastrophe of the past 10 years (in 2009, the central bank issued a 100 trillion Zimbabwean dollar banknote that was worth about $30 in U.S. currency) and given Zimbabwe’s repression. Gay male sex is illegal, and Robert Mugabe, Zimbabwe’s dictator, is scorching in his denunciations of homosexuality. “There is probably still fear of the health system,” said Ben Cheng, who researches diagnostic tools for H.I.V. at the London School of Hygiene and Tropical Medicine, and spends a lot of time in Zimbabwe. Gay men there, he says, “are probably not coming in to be tested.”

Still, here’s what Zimbabwe has done right:

It put its own money into fighting H.I.V. In 1999, the country instituted a 3 percent tax on income and corporate profits to fund AIDS programs. That continues, although the totals collected have suffered in synchrony with a failing economy. But few other poor countries have tried to do as much to pay for fighting the disease.

Some of the country’s leaders on H.I.V. are serious and competent, including Tsitsi Apollo, who directs the country’s response.

Deborah Birx, the United States’ global AIDS coordinator and head of Pepfar, said that the biggest global challenge is the first 90 in the 90-90-90 formula: getting people tested so that they know their H.I.V. status. It’s especially difficult to reach young people, so Pepfar focuses on them. “More than half of men under 35 and almost a third of women under 25” who have H.I.V. don’t know they’re infected, Birx said. “So they’re unintentionally passing it on.”

These groups are a priority in Zimbabwe as well. The country has a widely praised program to help adolescents stay on treatment, employing H.I.V.-positive teens as front-line workers.

And if men won’t come to the health clinic, the clinic goes to them. Mobile testing and even circumcision teams go in the afternoon and evenings to shopping centres, bars and other places where men congregate. (Male circumcision offers some protection against H.I.V.) “Men can now get circumcised at night at their favourite watering holes!” the Hatcliffe Polyclinic advertised.

But there’s a lot Zimbabwe still must do. “When we sit in committees with the National AIDS Council, it seems that everything is in place,” Tholanah said. “But in the communities, you find out there are such a lot of things communities lack.”

She said that clinics don’t talk to patients about managing the side effects of medicines. Labs frequently lose blood tests, and when the tests do come back, it’s with absurd delays. The results from one of her blood tests, taken in April, arrived in August, she said.

Perhaps most important, money is so short that needed drugs are not always acquired. One is fluconazole, an important drug that treats thrush and other fungal diseases in AIDS patients. Cheng visited a number of health centres and found that almost none had the drug. “They’re doing a much better job managing antiretrovirals,” he said. “But with drugs for opportunistic infections, stock-outs are still a common occurrence.”

Tholanah said that even some antiretrovirals are now going missing. “When things are O.K., people go every three months,” she said. “But of late, they’re not O.K.” She said that for some second-line drugs, clinics are giving out only a week’s supply and that she had heard of people getting only three days’ worth.

So they have to go back to the clinic over and over, which means paying for transportation, paying that dollar and enduring a long wait. Patients have started sharing drugs, she said. “And yesterday I heard that even for first-line drugs, they’re now giving a one-month supply,” she said. “That’s a red flag.”

Until recently, funding H.I.V. medicines worldwide looked like a noble, necessary — and never-ending — project. Now we know that treatment is prevention. Do it wide and well enough, and AIDS could be defeated. “This program started as a humanitarian outreach effort to demonstrate the compassion of the American people,” Birx said of Pepfar. “Now it’s translated into a program controlling the epidemic.”