I'd like some input on something I'm trying to model. I want to consider a population of people P, who all want to move to a new country. Let's say we have 5 countries (A,B,C,D,E) that all these people want to go to. Naturally I've given all these countries a carry capacity with a logistic growth equation. I have also made country A more attractive to move to than country E. So the flow rate from P into A is higher than the rate from P into E. When A reaches capacity people are obviously forced into the remaining countries.
Here's where I'd like some input. When more room is available in country A for example, people from P will want to move to A, BUT, people from B-E will also want to move there since they didn't have the opportunity to before since it was at capacity.
How would I go about representing competition between P and B-E for spots in A. Am I looking for a Holling type equation or maybe a probability term ? I've also looked into perhaps using some predator prey type model as the people are all "hunting" for a chance to be in A. I'm quite sure I need a functional response term of some sort, but deciding what models this situation best is a bit tricky.
Any ideas are greatly appreciated.
Many Thanks.