is similar to
gradually intrusive without right or permission
"we moved back from the encroaching tide"; "invasive tourists"; "trespassing hunters"
is similar to
intrusive in a meddling or offensive manner
"an interfering old woman"; "bustling about self-importantly making an officious nuisance of himself"; "busy about other people's business"
is an attribute of
aggressiveness as evidenced by intruding; by advancing yourself or your ideas without invitation