What type of schizophrenia does Mr. Ayers have in The Soloist?

There are several different types of schizophrenia, and they each can have wildly different manifestations. Nathaniel Ayers is a real individual, and he was diagnosed with a form of paranoid schizophrenia. Paranoid schizophrenia leads to severe paranoia of one form or another; often, individuals with this particular type of schizophrenia think that people are pursuing or threatening them. These individuals may also believe they are incredibly important or powerful (delusions of grandeur).
In Mr. Ayers's case, he had deeply rooted paranoia that rendered it very difficult for him to cope with everyday life. This led to him dropping out of Juilliard, in spite of his prodigious talent, and being unable to secure and hold down employment. Additionally, he constantly rejects Lopez's attempts at helping him, because his paranoia leads him to doubt the man's sincerity and intentions.