Exponential Growth on first half of a chessboard – Credit Wikipedia
Later today the CDC will officially unveil their estimates on the potential growth of the Ebola epidemic over the next four months if effective actions aren’t taken - and if it matches the leaked numbers published over the weekend in the Washington Post - it will run somewhere around 500,0000 cases.
For some, seeing that it took 6 months to reach the first 6,000 cases, jumping to a half million over the next four months may seem unrealistic.
Overnight Dr. Jody Lanard, who along with her husband Peter Sandman are considered among the most authoritative in the world on the subject of risk communications, posted a very helpful brief look at the power of exponential growth on her Facebook page that I’ve lifted (with her permission).
Re: CDC "model" of Ebola case numbers due out tomorrow: I have no capacity to assess the fine points of any mathematical model. But I can do plain arithmetic. So here goes: IF Ebola cases are truly doubling about every three weeks, and IF there are about 6000 cases so far as of today, and IF the doubling time remains the same for the next five months, here is what simple arithmetic shows:
Today: 6000 cases.
October 13: 12,000 cases.
November 3: 24,000 cases.
November 24: 48,000 cases.
December 15: 96,000 cases.
January 5: 192,000 cases.
January 26: 384,000 cases.
February 16: 768,000 cases.
So tomorrow, IF CDC ends up predicting around 550,000 cases by some time in January based on their more technical and refined model, it really matches pretty well with the simple arithmetic above. By the time you are doubling in the 6 digits, a million and then two million are not far off -- even if your starting number doesn't exactly match your model.
The rub, of course, is we don’t really know how many cases there are in the three affected nations of Liberia, Guinea, and Sierra Leone. The roughly 6,000 figure, offered in the WHO’s latest update, only represents `counted’ suspected or confirmed cases.
Today’s real number could be double or triple that.
We’ve seen estimates over the past month that range from 20,000 to 500,000 cases by early next year. Admittedly a huge range of outcomes, but the truth is, how this turns out all depends upon the effectiveness (and speed) of the international response.
There are a lot things that can successfully mitigate or influence this epidemic, including the use of isolation and quarantine, contact tracing (which admittedly becomes more difficult as cases rise), the universal use of PPEs by HCWs, community education and modification of dangerous practices – and the eventual introduction of therapeutics & vaccines (although we are months away from seeing that).
Other factors, including population size and density, geography, and opportunities (or lack thereof) for the virus to jump to new regions can all influence the rate of growth and outcome of this epidemic.
True exponential growth obviously cannot be maintained forever, or even for very long. The graphic at the top of this blog represents the classic doubling (starting with 1) on each of the first 32 squares of a chessboard. It takes between 12 and 13 iterations to get to where we are now – roughly 6,000 cases.
From here, it takes only 6 more iterations (approximately 18 weeks) to get us to 524,000. Three weeks later you are at a million, and from there . . . .
I don’t pretend to know who’s estimate is right. But the takeaway from all of this is - if this Ebola epidemic isn’t brought under control relatively soon - it isn’t inconceivable that millions in West Africa could be infected over the next year.
And where it would go from there is something that no one wants to think about at this stage.