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May 13, 2003

A public radio commentary

I have several friends and colleagues returning from Asia right now, and some leaving for China. So, I took a careful look at the mathematics of SARS - Severe Acute Respiratory Syndrome. The mathematics used to study disease is called epidemiology. Its goal is to create a vivid picture of a disease in space and time. For example, at first SARS seems like a tiny thing. Right now, there are about 7000 cases in the world, and about 400 people have died. Each death is tragic, but it seems small compared to a world population of billions. But here is where an epidemiologist paints a precise picture that changes this naive view.

First, they look at the kind of people who are getting ill. For SARS the young and healthy people have suddenly become critically ill. This alone causes alarm. Next, an epidemiologist measures how it spreads: SARS began in the Guangdong Province of China and has rapidly reached four continents. Another cause for alarm. And lastly, they look closely at the growth rate.

They tabulate every day the number of new cases, and then compare it to the previous day to see how quickly SARS is growing. They are watching to see whether the growth is what they call linear or exponential. Linear growth is normal constant growth. For example, a child between the ages of six to thirteen grows the same amount every year - about four inches. This is called linear growth, because it's the same increment every time. Contrast this to exponential growth, which is quite astonishing.

It's captured best in an ancient legend about the inventor of chess. His king loved the new game of Chess, so he summoned the inventor and asked what reward he would like. The inventor requested that one grain of wheat be placed on the first square of the chess board, two grains on the second square, four grains on the third, and so on until all sixty-four squares were covered. The king, thinking this a modest reward, ordered his servant to fulfill the request. To his surprise, all of the grain in his kingdom couldn't fill the board. By the end, the number of grains on the last square would be a nine followed by eighteen zeros. This is the power of exponential growth.

So, if each increment of growth for the number of cases of SARS grows larger than the last - this exponential growth - then we likely have a nasty epidemic on our hands. Right now it is growing linearly, there are about 250 new cases added every day. Not that less than exponential growth means the world is safe, but it seems that this isn't the big one scientists have been watching for - like another 1918 influenza, which killed twenty million people.

Yet, I suggest you keep plotting the numbers yourself and watch carefully the growth rate of SARS.

Copyright 2003 William S. Hammack Enterprises