I used to teach in a preschool/daycare. Biting is a really big deal in those environments because it's so "contagious" and, of course, it hurts. They usually will kick someone out for it if it continues for a while. We usually gave it some time, but if your school get a lot of parent complaints, they will have to deal with it. Nothing makes a parent more upset than finding out their kid was bitten during school. Parents want immediate action a lot of times.
Most of the time, it's a communication thing. I would see it a lot in kids that weren't able to express themselves, and a lot of times the child being bit was one that was quite proficient with his/her language skills. The biter almost feels it's an unfair fight, and does what they can to keep up.
You don't see it a lot with the 3's because, usually, they are a little better at expressing their feelings. They can defend themselves with their words. Maybe work on teaching him the right words to use. If he's upset, and yells or screams, teach him to take a breath and help him to label his emotions. Don't give him anything without him asking for it with his words...milk, snacks, etc. In general, just encourage him not to be physical...set the example all of the time. If he yells at you or hits or pushes you or the dog or brother or sister...take him aside and explain why it's not okay and walk through it with him again.
As far as the biting...the minute you see him after school, deal with it. If they say he bit someone, get down on his level, in his face and say "No biting"...very firmly. We always used to say babies bite, animals bite...are you a baby or an animal? Good boys and girls use their words...biting hurts...do you want to hurt your friends? Biting is wrong." We would repeat it a few times. Obviously, we never did the biting back...we are teachers...not really okay to bite someone's kid!
Good luck...it'll pass. You don't see too many high schoolers biting!