He appears to be a parody of the character, Hannibal Lecter, from the crime novels by Thomas Harris, with similar hairstyles, mannerisms and voice, and the need to be kept under maximum security.
Joshua easily psychologically manipulated Officer Barbrady to get what he wants from him in a similar fashion to the way Clarice Starling is manipulated in Silence of the Lambs. When let out of his cell, he was strapped to a hand-cart with a special mask.
He has thin eyebrows, long blackish hair, a light blue suit and black shoes. His eyes are not joined together, possibly as a reference to the appearance of Anthony Hopkins as Hannibal Lecter.
He is somewhat manipulative, even making Officer Barbrady break down in tears, although, this could also be explained by Barbrady's low intelligence. Josh is also clearly a 'bad boy', if you will, being in juvenile hall and toilet papering over 600 houses in one year, as mentioned by the police officer. Otherwise, Josh is tough and sneaky, able to break out of the metal hand-cart (although he only had three weeks left before his release).
Josh also has an obsession with upping his game at the mere sight of toilet paper. Once broken out, the last seen of him was himself approaching the white house, armed with two boxes of Toilet paper.