To dream of madness or seeing a person who has gone mad may represent feelings about yourself or others having lost their senses to an obsession. Having “gone mad” crazy in love for someone to point of causing problems. Being emotionally incapable of getting your mind off something or someone. Unconventional behavior.
Negatively, it may reflect a tendency to totally embarrass yourself being obsessed with something. Humiliating yourself being too in love with someone. Feelings about yourself or someone else having behaved in an inappropriate manner.
Seeing your boyfriend run mad in your dream can go in two different meaning here.
If he is mad, as in just mad 😢, it implies that your relationship is at risk, and he will be the one to break the egg on your face. In a simple sentence, he will get angry at you and break up!
On another note, if he happens to chase you in the dream as a mad man, Oh dear 😇, he is madly in love with you. Is up to you to accept his mad love in act.