Let poorer countries pay to train nurses and doctors, and then wealthier countries take the best because they can pay more for them due to economic dominance.
We do it in New Zealand by importing a lot of doctors (Chinese and Indian seem common), and nurses . The reason we need to import doctors is because we export a lot of doctors and nurses to wealthier countries such as the USA.
In New Zealand, we get people from poorer countries because we can pay more, and we also get people from first world countries because people want to move here for the lifestyle or for their children.