Thursday, January 28, 2010

S Z R Models

I introduced the basic SIR model for a simple epidemic to you. this model actually has a long history and was first described by Kermack and McKendrick in 1927.

As I indicated this model has since been expanded to include virtually every disease scenario you can imagine.

Last year a group of Canadian mathematicians used this SIR format as the basis for an analysis of a zombie epidemic. Their paper: WHEN ZOMBIES ATTACK!: MATHEMATICAL MODELLING OF AN OUTBREAK OF ZOMBIE INFECTION ) - somehow it seemed appropriate to keep that in capitals) - describes a model that should look basically familiar to you.

Notice in their S Z R model (Z for Zombie of course) there are two extra transitions - from R back to Z (reanimation of the dead is well established in the zombie movie genre) and a movement directly from S to R (non zombie related death).

This is, perhaps unsurprisingly, the first mathematical analysis of an outbreak of zombie infection. While the scenarios considered are obviously not realistic, it is nevertheless instructive to develop mathematical models for an unusual outbreak. This demonstrates the flexibility of mathematical modelling and shows how modelling can respond to a wide variety of challenges in ‘biology’.

In summary, a zombie outbreak is likely to lead to the collapse of civilisation, unless it is dealt with quickly. While aggressive quarantine may contain the epidemic, or a cure may lead to coexistence of humans and zombies, the most effective way to contain the rise of the undead is to hit hard and hit often. As seen in the movies, it is imperative that zombies are dealt with quickly, or else we are all in a great deal of trouble.

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