Derek is suffering from a severe mental illness that is characterized by distorted thought and perception. he hears voices in his head and is convinced that aliens are trying to communicate with him. derek's belief is so strong that he sits on the roof for hours having conversations with no one in particular. derek is also in the habit of writing words that make no sense and refrains from interacting with other people. in the context of dissociative disorders, it can be inferred that derek is most likely suffering from in this scenario.

The answer to this question is the "SCHIZOPHRENIA". Hence when Derek is suffering from a severe mental illness that is characterized by distorted thought and perception. And when he hears voices in his head and is convinced that aliens are trying to communicate with him. Also, if  Derek's belief is so strong that he sits on the roof for hours having conversations with no one in particular. Additionally, Derek is also in the habit of writing words that make no sense and refrains from interacting with other people. in the context of dissociative disorders, it can be inferred that Derek is most likely suffering from  SCHIZOPHRENIA in this scenario.