Slate has a neat article about Facebook’s new “25 things about me” craze. (For those who have remained blissfully ignorant: thousands of users wrote notes about random personal habits or goals, and tagged their friends in an expanding web of navel-gazing.) Turns out it can be modeled like an epidemic. A user is “contagious” for about one day — the day he tags a bunch of his friends in the note. After being tagged, most users respond within one day. Then response frequency drops off exponentially.
Here’s a nice Nature Review about the mathematics of modeling infectious disease.
The number of individuals that an infected person infects is given by a probability distribution. The probability that an infected person will infect another person within a small interval is
b(t) s dt
b is infectiousness, dt is an arbitrarily small amount of time, and s is the probability that the other person is infected.
If a group of individuals all have the same infectiousness, then the number of secondary infections that are caused by each infectious individual is a random number drawn from the Poisson distribution with mean R, where R is the expected number of new infected victims.
The interesting thing here is that the whole field of mathematical modeling of disease transmission isn’t going to be just a biological subject forever. It’s also going to be a behavioral subject. The idea that cultural ideas propagate and evolve like organisms isn’t new — it’s as old as Dawkins and his notion of “memes.” But back in the sixties he couldn’t have predicted just how concrete the similarities would be — that we could see the exact same differential equations governing Facebook crazes as malaria outbreaks. Watch as epidemiologists get drafted as marketing consultants in the next few years.