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Facebook, evolution, and mathematical modeling

In Biology, Delights, Math on February 12, 2009 at 6:09 pm

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.

biological infectiousness of influenza, HIV, and malaria

biological infectiousness of influenza, HIV, and malaria

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.


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