When did we start talking about "going viral"?

I am trying to determine when the phrase "going viral" was first used. Similarly, when did the phrases "viral video" and "viral marketing" get their start? I have looked online at various sites, but none really address this question (other than saying "recently").

The Oxford English Dictionary's earliest citation for the use of viral in the sense of ‘involving the rapid spread of information’ is dated 1989. The earliest citation actually including the verb go is as late as 2004:

Their petition also went viral, gathering half a million signatures in a few weeks.

It looks like the phrase started being used in print in about 1999 or 2000. And viral video seems to date from 2004.