I'd be interested if you have done any analysis on the topic.

I haven't, because it seems obviously false to me. Africa's population has been growing exponentially over the 20-21st centuries, aid to Africa has not, as far as I know. If conditions in Africa were so bad that aid contributed only a fixed number of life-days - if it only saved people to die another day, then I would not expect to see continued exponential growth but rather, re-hitting the Malthusian ceiling and quickly.

(One could try to explain this by saying the life expectancies and public health changes are thanks to non-aid Western inputs like regular commercial goods, but this strikes as an ad hoc explanation to try to deny the value of aid.)