The forgotten diseases of the poor world are finally getting some attention. Warren Buffett’s $31 billion donation to the Bill and Melinda Gates Foundation is just the latest and most spectacular milestone in an increasingly aggressive campaign against infectious diseases, including tuberculosis, malaria, and HIV/AIDS. But even as the rich world finally grapples with this challenge, a new and more menacing threat to the developing world’s health is gathering.

Chronic ailments such as diabetes, cancer, and heart and respiratory disease are hitting poor countries faster and harder than expected. Perversely, economic growth and development is hastening the arrival of rich-world diseases before poor countries’ health systems can prepare.

Revolutionary changes in transportation, advertising, and food production have conspired to alter lifestyles abruptly in many parts of the developing world. Popular Western junk food, cheap cigarettes, and a flood of new automobiles mean that many citizens of poor countries eat worse and exercise less than they did only a decade ago. The movement of people from the countryside to more lucrative jobs in the cities has exacerbated the trend. Public health awareness in most poor countries hasn’t caught up. This new affluence means that the poorest countries are now fighting a two-front war on disease.

Diabetes—a disease usually associated with affluent societies—is particularly dangerous. In countries with weak health infrastructures, it is anything but the manageable condition it can be in the rich world. A person in Mozambique who requires insulin injections, for example, will probably live no more than a year. In Mali, the average life span after onset is 30 months. According to the International Diabetes Federation, the number of people around the world...