As of today, there is no official support for what you're looking for, which in UI Router parlance is considered 'dynamic parameters'. However, if you check out this experimental branch and help us out by testing and providing feedback, it will get merged to master sooner.
Set up your route/state like so:
$stateProvider.state("country", {
url: "/country/{id:int}",
params: { id: { dynamic: true } }
/* other state configuration here */
});
Then, in your controller, you can observe changes to id
like so:
$stateParams.$observe("id", function(val) {
// val is the updated value of $stateParams.id
// Here's where you can do your logic to fetch new data & update $scope
});