Infant mortality is definitely one. There's a team from Stanford who developed a baby warmer for areas where electricity is an issue http://blog.ted.com/2010/07/09/fellows_friday_4/http://www.ted.com/talks/jane_chen_a_warm_embrace_that_saves...
Even if you go for a different problem, it's an interesting case to look into method-wise - I read somewhere else about how they iterated based on feedback from local community but I can't find it...