It usually occurs in older people. – Is okay because it's describing a demographic.
It rarely occurs in younger people. – Is okay for the same reason. "~younger people" is a demographic and matches the context.
It rarely occurs in a younger person. – "~in a younger person" suggests one person, or an example which is confusing in the context of your sentence because you're describing the features of an illness in a general way. Say: "It rarely occurs in young people."
If you must use the phrase "in a younger person", maybe change the sentence to "It would rarely occur in a young person". "It would~" suggests a hypothetical situation, so a specific subject would make sense.