Autism: a disorder of neural development characterized by impaired social interaction, by impaired verbal and non-verbal communication, and by restricted, repetitive or stereotyped behavior.
Will Graham describes himself as having a "horse hitched to a post that is closer to Asperger's and Autistics." Although society seems to focus specifically on the small amount of Autistics who have extreme cognitive dysfunction as the central aspect of Autism, the Hannibal series is quite different and does not portray Will as a unable to function independently (Note: The majority of people with Autism function normally as anyone else would).
Despite his mental illness, Will is able to teach college classes and assist the FBI with murder investigations. The only characteristics of Will we see as the audience are his dry humor and quick wit. Characters such as Jack Crawford are portrayed as 'stepping lightly' with Will at first, but that behavior is short-lived and disappears almost immediately within the first few episodes.
Because many cinematic stereotypes paint a violent picture of Autistics (such as One Flew Over the Cuckoo's Nest), a negative-- almost fearful-- connotation has developed. Having a psychological understanding of Autism, however, allows a person to understand that someone such as Will Graham can have Autism and still function relatively normally, and this is by far no miracle that Will Graham is able to do so.
Encephalitis: an acute inflammation of the brain (Acute in medical cases means with a rapid onset or short course).
Relatively in the middle of Season 1 of Hannibal, Will Graham is taken in to get an MRI Scan on his brain, due to the suspicions of Hannibal in a previous episode (the clock drawn above is a common mediocre test used to test for signs of encephalitis). Since the beginning of the series, Will Graham displays signs of the inflammation such as headache, fever, confusion, drowsiness, and fatigue. Will also experiences the more onset symptoms such as convulsions, tremors, hallucinations, memory problems, and seizures (although it is revealed in Season 2 that Hannibal was using seizure-inducing strobe lights to alter Will Graham's memory).
With knowledge of encephalitis, a person would have been able to see Will's illness as early as Hannibal's suspicions arose early in Season 1. We would also be able to see the correlation between the intensifying of Will's hallucinations (from nightmares to full-blown images during the day) to the further worsening of the inflammation in Will's brain due to the encephalitis.
Hallucination: an experience involving the apparent perception of something that is not present.
From the beginning of the Hannibal series, the audience witnesses Will Graham's hallucinations. Most of these visions are motifical, occurring many times throughout the season. The most common one is a black stag with the feathers of a bird as opposed to fur (as seen below) that the fan base has named 'Swiggity Swag the Nightmare Stag'. Although a fitting name, it seems to represent Will's conscience throughout the show, oftentimes leading him to a destination or mirroring his physical actions. The second motifical hallucination is the Hannibal Deer (as seen above). This character shows up simultaneously in Will's dreams and hallucinations, sometimes watching and sometimes harming Will himself or Swiggity Swag. The Hannibal Deer represents Hannibal Lector obviously. The physical features match up exactly, except the hallucination is completely void of color. The Hannibal Deer remains objective as Hannibal does when speaking with Will, but also attacks Will's conscience, as he does by manipulating Will's mind (and also sending someone to kill Will). In one episode of Season 2 when Will's hatred towards Hannibal finally surfaces, one of Will's hallucinations involves Will murdering the Hannibal Deer, showing his thoughts of harming Hannibal in real life.
Oftentimes Will's hallucinations will change based off the murder cases he solves. In a previous episode, a psychopathic murderer would kill his victim, place a live bird in their chest, and place the body in a horse's belly as their idea of 'rebirthing' that person. As seen in the pictures below, Will's hallucination has not altered to himself being reborn out of Swiggity Swag.
Through a psychological scope, one can see many possibilities as to why Will Graham experiences such vivid hallucinations. One idea is that it is caused by encephalitis. Hallucinations is one of the key symptoms and it would also explain why Will's visions seem to get more potent and reoccurring as time goes on (the encephalitis is worsening). Another possibility is Will Graham is experiencing PTSD. In order to get an accurate profile of a killer, Will is envisioning countless murders in the eyes of the killer. It clearly begins to take a mental tole on him when the series advances and another psychologist even suggests to Jack Crawford that they stop using Will so much in the investigation process. Regardless of the fact, mentally murdering dozens of people would take a tole on anyone, let alone someone with an already unstable mind.