Nairobi, Sept. 10 -- Early in Alice Kang'ethe's public-health career, on a trip to Mbita, a scorpion stung her. The pain was ferocious. She was far from a proper hospital, and her international health insurance was useless there. The immediate help at her disposal was a modest clinic, where health workers gave her an antidote and got her the care she needed.

"Those people saved my life," Alice says. It is, in a way, the whole argument she has built a career on: Fix the small clinic, and the rest of the country survives with it. Ignore it, and geography decides who lives.

Alice has spent 20 years chasing that idea across borders, first as a volunteer in Dar es Salaam. She had just returned from the London School of Economics (LSE), hopin...