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SARS Growth

Via David Smith, a statistical graph and predictions for the SARS epidemic by Ted Kaehler:

2003-04-06-01.gif

The number of reported cases of SARS in the world is doubling every 11 days. This is implied by the slope of the blue curve, using the data available on April 5, 2003. There will be 100,000 cases on about June 1, 2003. A million cases will be reached on about July 6, 2003, and ten million on about August 11, 2003. These predictions will change every day as new data changes the slope of the curves. Only world cases after March 25, 2003 are used to compute the slope, because that is when China began reporting...

Epidemics usually follow S-shaped curves. The predictions here are based on pure exponential growth. When the middle of the S-shaped curve is reached, the rate of infection will slow, and exponential growth predictions will no longer be useful. The reported data shows that the epidemic is still in an exponential growth phase.

The $64,000 question is, when will SARS transition out of its current exponential growth phase and into the middle of the S-shaped curve? After 10,000 cases? 100,000 cases? 1,000,000? 10,000,000?

The page with the graph and all the statistical forecasts can be found here.

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Comments

So, have you re-calibrated your model with new data in the last two weeks? (it is now April 21). Are we tracking somewhat lower than your model would have predicted?

Craig, I wish I could take credit for the model, but I can't. It's from Ted Kaehler.

Ted updates his model (which you can find here) as the WHO releases more information (at 1700 GMT every day except Sundays, I believe). His last update was two days ago. As of 6 April, SARS cases were doubling every 11 days. As of 19 April, they were doubling every 17 days.

Ted points out that all epidemics follow an S-shaped curve. The question is when we hit the part of the curve where growth flattens. It could be that we're there already, or it could be that Chinese underreporting of cases has distorted the true shape of the curve and that we're still trending sharply upwards.

Good Morning,

I was very interested to see that someone has taken the time to predict the spread of this outbreak.

I was wondering if you could give me some informed advice on matters of travel. I and my colleagues are to travel to India this year, we are then intending to travel through Vietnam, Cambodia, Thailand, Malaysia and finally ending up in Singapore. Our Asia leg will be starting in AUGUST 2003, lasting approximately 4 months.

I was wondering if you could give me any prediction on how serious this could become or perhaps shed some light on the subject!

Thank you for your time.

Mark Lewis
UK

Mark, I'm unqualified to offer any sort of medical advice to you in your travels. May I suggest some sites for you, though?

The US Centers for Disease Control's SARS site can be found here. The World Health Organization's SARS site can be found here. The UK Department of Health's SARS site can be found here.

All three organizations have detailed information on SARS along with travel advisories. These advisories differ by organization -- for example, the WHO recommends against non-essential travel to Toronto, while the CDC simply advises visitors to avoid Toronto-area hospitals. You'll have to compare the information and make your own best judgement.

Having an exponential scale on the y - axis makes it difficult to determine when the curve is flattening and beginning to decline, as in the typical epidemic curve, which usually follows a positively skewed normal distribution when only new cases are plotted over time. This graph of cumulative cases actually gives less information.

Michael, the exponential scale of Ted's chart makes it extremely simple to determine visually whether the SARS epidemic is increasing at an exponential rate. That was his goal.

If you want linear scale graphs, you can find links to them (for Canada and Hong Kong) at the bottom of the linked page.

G'day!

Just stumbled on this site and thought I could let u know about my own little predictions (not to be taken toooo seriously though)...

www.lb-netz.de/SARS2003.doc

comments are welcome!

lutz

Hey I was just wondering if you had the actual data for the cases. Dates, countries, things like that. If you did could you possibly send them to me. Or at least let me know where I would be able to find them
Much Thanks
Nathan

Nathan, have you searched the CDC and WHO SARS sites? The URLs are listed in one of my comments above.

Unfortunately I dont believe that this disease is likely to pull back quite as suddenly as some expect. As for the general dynamics of disease transmission it should be noted that during the early stages of disease tranmission you may see the signs of growth and decay that would give one the impression of a flattening out, but this may well be deceptive, just as when an airplane first takes off, and you feel a momentary drop off, and rise many times during the ascent to cruising altitude. I mean therefore that if this is the big one, I would not expect to see real evidence of the S-Shape any time soon, and periods of marked growth and occaissional decline, would more than likely be evident in the opening stages.
The worst phenomenon has not yet been seen, which is that of the a-symptomatic carrier. If this is a fact then the likelyhood is for a very tough time with SARS.

This is pretty interesting. I agree with the author.


Nice post:)

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