As said they'll die off, as all do. We do experiance spammers attack from time to time, although I must say there haven't really been many in past few months (at least that I know of).
At this point I'd like to say how great ranks deal with spammers, although from time to time they also spam the chat. When attack emerges, one should (someone who's not too busy, most focused on chat) kick the spammers, to avoid extra spam.
I don't find those attack too frustrating, but I notice a lot of people leave chat when they occur; I believe there isn't option to IP ban someone from chat? The only legal actions we can do is to report all 'spam accounts' and maybe contact Jagex via forums - sure they'll take actions against IP, I hope so.
Continue great work!