Friday, September 26, 2014

Exponential Outbreak

Epidemiologists have a number they use to describe the average number of people each infected person goes on to infect, to describe the rate of growth of an outbreak.  It's called the effective reproduction number, and it looks like this, where "t" is the number of subsequent infections: Rt

An R of 1 means that the outbreak is steady (and still possibly manageable); one person infects one other person, who then infects one other person, and so on.  If, on average, each person proceeds to infect less than one person the outbreak can be expected to diminish.
An R of 2 means that each person infects two other people and the outbreak will double in new infections every incubation period (which, in the case of Ebola, is thought to be around 12 days).
From June to July of this year, the Rt in Liberia was estimated at 1.7 and reports since then have not indicated an improvement.

I have a hard time directly understanding exponential growth when I see a line chart that curves up rapidly.  I mean, I get it, but an upward trending line is a pretty abstract representation of human suffering.  To illustrate, largely for myself, what exponential growth looks like outside of a line chart, I made an image that shows a hypothetical R2 (doubling) with a twelve-day incubation.
I stopped after 180 days, but thereafter is when the numbers become staggering.

Here is a graphic from one month ago comparing the then-smaller outbreak to all other known Ebola outbreaks.

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