WordNet sense 1 (involving invasion or aggressive attack):

incursive, invading

WordNet sense 2 (gradually intrusive without right or permission):

encroaching, trespassing

WordNet sense 3 (tending to intrude (especially upon privacy)):

intrusive

WordNet sense 4 (for the purpose of attack rather than defense):

offensive

WordNet sense 5 (tending to spread quickly):

aggressive