"If you are infected and infect someone else, the number of people this 'someone else' will infect … is the number that tells you whether the campaign or infection will be alive in the second round or not," Moro said. "As long as the fast forwarders who first get wind of the news spread it to more people than originally heard it, it's over the tipping point."
"If you're above the tipping point, the message not only spreads out to a large fraction of people of society, but [does so] in a matter of hours," Moro said. "Not because the message is important, but because the more active people are the ones driving the information diffusion."
This results in a viral phenomenon like the videos of Susan Boyle singing on Britain's Got Talent, which reached 47.7 million people in less than a week.
About 90 percent of viral marketing campaigns fail to reach this tipping point, but they're often cost-effective because they may continue to spread, although at a much more casual pace. Below the tipping point, slowpokes take the reins, as they have in the case of the Veuve Cliquot champagne hoax.
Moro's experimental campaign lasted two months after the original emails were sent; his model predicted it would persist for a year if he maintained the website supporting the campaign.
But companies who want to use viral marketing to keep costs down, Moro said, should decide quickly whether to kill a campaign or keep it alive.
"If you're in a viral marketing department, you want it fast, cheap, and big," Moro said. "What we're telling them is run it for two days."
By that point, the campaign will spread to half the people it will ever reach; the other half will trickle in gradually over months, dragged out by the slow forwarders. If reaping the benefits from these late-comers requires maintaining a website or some other cost, it might not be worth it.