How to get the KClass for a Kotlin constructor parameter

Using Kotlin reflection, I am trying to check the KClass of each parameter of a class's primary constructor.

Given a simple data class like this:

data class MyPerson(val name: String, val age: Int)
val modelClass = MyPerson::class

I get its primary constructor val primaryConstructor = modelClass.primaryConstructor. For each parameter, I want to check its class (is it Kotlin.String, Kotlin.Int etc). Something like this:

for (param in primaryConstructor.parameters) {
  when(param.type) {
    is Kotlin.String -> // do string thing
    is Kotlin.Int -> // do int thing
}

Unfortunately, this isn't valid code. I've tried param.type, param.classifier, param.type.jvmErasure and others. The closest I've found is param.type.jvmErasure.qualifiedName, which gives me a String with the fully qualified name of the KClass. But I really want the KClass.

Is this possible at all?