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Friday, April 21, 2006

The correct use of the logistic curve

An interesting simulation (via DailyKos) of avian flu pandemic dynamics demonstrates the correct application of the logistic curve. Contrary to what old-school oil depletion analysts will tell you, the logistic curve (aka Hubbert curve) has no place in modeling a depleting resource, yet finds a much better fit in contagion dynamics. I took the following snapshot from a movie of the LANL simulation after the infected population reached a peak and had fully declined.

If you look at the lower left curve and compare it to a generic logistic curve1, it fits (apart from a weak asymmetry) fairly well.

If you slide the one over the other, you can see the rather minor differences.

Sorry to have to hammer the point home with such an unpleasant scenario, but oil depletion has nothing in common mathematically with the derivation of contagion dynamics, and really nothing to do with the logistic curve. The contagiousness of oil exists only in our simplistic, close-minded imagination.

1Thanks to David for pointing out a minor error in the derivation.


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6:04 PM  

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