Partners in Health, the Boston-based health charity, which runs two rural hospitals and a network of smaller clinics in Rwanda, said its own costs ran $28 per person per year in areas it serves. It estimated that the government’s no-frills care costs $10 to $20.

According to a study recently published in Tropical Medicine & International Health, total health expenditures in Rwanda come to about $307 million a year, and about 53 percent of that comes from foreign donors, the largest of which is the United States. One big donor is the Global Fund to Fight AIDS, Tuberculosis and Malaria, which is experimenting with ways to support whole health systems instead of just treating the three diseases in its name. It pays the premiums for 800,000 Rwandans officially rated as “poorest of the poor.”

In a nation of poor farmers, who is officially poorest is decided by village councils. They weigh assets like land, goats, bicycles and radios and determine whether a hut has a costly tin roof or just straw.

“People know their neighbors here,” said Felicien Rwagasore, a patient coordinator at the Mayange clinic. “They do not make mistakes.”

Making every Rwandan pay something is part of President Kagame’s ambitious plan to push his people toward more self-reliance and, with luck, eventually into prosperity. The country has been called “Africa’s Singapore.” It has clean streets and little crime, and each month everyone does one day of community service, like planting trees. Private enterprise is championed, and Mr. Kagame has been relentless about punishing corrupt officials. In the name of suppressing remarks that might revive the hatreds that spawned the 1994 genocide, his critics say, he suppresses normal political dissent, too.

A more practical obstacle to creating a health insurance system, however, is that most of the world’s poor, including Rwanda’s, resist what they see as the unthinkable idea of paying in advance for something they may never get.

“If people pay the $2 and then don’t get sick all year, they sometimes want their money back,” said Anja Fischer, an adviser to the Health Ministry from GTZ, the German government’s semi-independent aid agency.