A year to the day after she buried her son, Joanie Halgrim rode in a minivan down a rocky dirt road not far from the airport in Nairobi, Kenya. Her stomach turned from the stench of rotting garbage and raw sewage mingling with exhaust fumes and the acrid smoke from sizzling meat peddled by street vendors.

The van stopped in the midst of some bleak gray apartment blocks, their balconies festooned with drying clothes flapping in the sun. She and the other travelers got out and entered an austere concrete block building. It didn’t look nearly finished, and yet in a week’s time it woul...