In poorer countries serious diseases more often than in richer countries result in death. Additionally, becasue the diseases are often untreated, they are not as contained as in richer countries, which means that they spread more. This means that smaller countries are more affected by diseases.
I think that US (and other rich countries) should have a moral (but perhaps not legal) responsibility to help. If not for other reasons, then for the reason that if diseases spread in poorer countries, they might also be brought to the US. Additionally, this would be a good example of human solidarity.