[Unfortunately the Cheat Sheet we promised a while back still is not available on this blog. If you want a copy, you need to email G. Sallust at opsrus@comcast.net. One will be provided on request. Normally I’d fire the incompetent responsible for the delay in posting it, but I am the culprit, and I need the work.]


Well, time marches on and Ebola cases continue to pile up. There’s a September 13 report on CBC [not CNBC, NBC, CBS or other U.S. networks] that says West Africa now has hit 4700 total Ebola cases. And there’s no sign that the current Ebola outbreak will stop growing any time soon.

Why is today’s version of Ebola so obviously more contagious than previous ones? Why do so many people who are protected with latex gloves, etc. seem to get it anyway? Could it be that today’s Ebola has new or augmented ways to transmit itself from human to human? Could it travel, for example, through the air on minute droplets of water, much the same way that the common flu virus does? Is anybody looking into the question, or is our medical establishment simply in denial? Or is the Government part of it trying to keep us, the public, from panicking this close to elections?

Anyway, the CBC report looks at some of these questions and discusses possibilities we don’t hear much about here in the U.S. It’s a video, by the way, and if you’re interested in following up you can find it at https://screen.yahoo.com/ebola-surging-beyond-control-whos-014636327.html

Last time, you may recall, we did a Cheat Sheet to project hypothetical results for the current epidemic:

  • One scenario assumed infections would double every 35 or so days for an indefinite period. We got that idea from a scientific report put out on August 28.[1] If infections continue at that rate for a couple of years, then the entire planet will be infected in two years. We called this a “geometric” growth rate.
  • The other simply added an equal number of cases on each day covered by the scenario, and ended with a total of 20,000 cases by mid-February of 2015. We got that idea, more or less, from the World Health Organization’s Roadmap for fighting the infection in Africa, also published on August 28.[2] We offered two versions of the WHO scenario; in one the disease is conquered and infections top out at 20,000; in the other infections continue, but only at the same rate as before.

Assuming total infections reached 4700 on or about September 13, as of now the current infection rate more than conforms to the “geometric” scenario. By a trick of the math, however, it hasn’t yet reached the level required by our second, linear projection. To do that, cases would have to increase to a total of 5,693 by September 21. Given that everyone seems to agree that whatever “system” there is for reporting cases grossly underreports[3], it seems highly likely that total Ebola cases will meet or exceed that number as well.

So how do we determine which scenario, if any, is correct? Answer: Wait until November. The “geometric” scenario calls for cases to double every 35 days or so, and that’s a very fast rate. By November new cases projected in the geometric scenario begin to substantially exceed the linear projections, and in early January are more than twice the more conservative numbers. Take a look at the Cheat Sheet, to see what we’re talking about.

So, you might ask, what does WHO think of all this? Do they like your “geometric” projection, or do they prefer the more conservative one you attribute to them. Well, it all depends on your definition of “geometric.” A geometric progression is a series of numbers, each of which is multiplied by the same constant. [4]  We thought that was the right description, where numbers in a series are doubled every 35 days. But there’s another way to describe the same thing. A series of increases like that also can be called “exponential.”[5]

It’s not correct to say that WHO “likes” or even knows about anything we’ve written here at Elemental Zoo Two. But they’re on the ground in West Africa, and it looks as though they’re coming around to the “geometric” mode of thinking, at least in the short term; but WHO uses the word ‘exponential’ instead. ”Transmission of the Ebola virus in Liberia is already intense and the number of new cases is increasing exponentially,”[6] WHO says. People fighting the disease in West Africa should prepare for that.[7]

OK, granted WHO thinks the growth rate is exponential. Even the CDC might agree. Early in September it said the epidemic was “spiraling upward.”[8] But just how fast is that? It’s not really clear, at least at the moment. Our “geometric” projection was based on information provided in the August 28 report in Science that studied the genetic makeup of Ebola.[9] When the data comes in – assuming we get reliable case counts – then we’ll all know. Until then, we’re just guessing.

And what about transmission? Is there anything to explain the upward spiral in cases other than, contrary to the popular wisdom, Ebola might be transmitted through the air? Well, yes, there are possibilities. WHO reports, for example, that taxis in Liberia’s capital, Monrovia, typically are not disinfected, ever, and could be a source of “contact” Ebola.[10] The BBC, on the other hand, reports Ebola is spread by direct contact, but also by “contact with contaminated environments,”[11] whatever that means. And, of course, it’s been known for some time that certain strains of Ebola can in fact become airborne[12]; apparently they just haven’t been caught making people sick when they do.

But if that’s currently true, what if the virus mutates, and develops the capability? There’s a very interesting opinion piece on that subject in last Thursday’s New York Times.[13] Apparently the virus mutates readily; it’s “sloppy in replicating”, and ‘[e]ach new infection represents trillions of throws of the genetic dice.”[14] A bigger, much worse Ebola might well come out of that.

Something to look forward to, I guess.



[1] See Sciencexpress Reports, Gire et al., Genomic surveillance elucidates Ebola virus origin and transmission during the 2014 outbreak (28 August 2014) (hereafter cited as Genomic Surveillance at __), available at http://www.sciencemag.org/content/early/2014/08/27/science.1259657.full.pdf

[2] See World Health Organization, Ebola Response Roadmap (28 August 2014) (hereafter cited as WHO Roadmap at __), available at  http://apps.who.int/iris/bitstream/10665/131596/1/EbolaResponseRoadmap.pdf?ua=1

[3] See CDC, Press Release, CDC warns Ebola epidemic in West Africa is outpacing current response (September 2, 2014) (hereafter Sept. 2 Ebola Press Release at __) available at http://www.cdc.gov/media/releases/2014/p0902-ebola-epidemic.html?s_cid=cdc_homepage_whatsnew_001

[4] See Answers.com, Geometric (citing the Oxford Dictionary of Units and Measures), available at http://www.answers.com/topic/geometric: ”Applied to a series of numbers, ‘geometric’ indicates that adjacent members differ by a constant multiplier, the ‘common ratio’ (any finite number). The geometric series with common ratio b has the form a, a•b1, a•b2, a•b3 … for some value a.”

[5] See Wikipedia, Exponential Growth, at http://en.wikipedia.org/wiki/Exponential_growth: “Exponential growth occurs when the growth rate of the value of a mathematical function is proportional to the function’s current value. Exponential decay occurs in the same way when the growth rate is negative. In the case of a discrete domain of definition with equal intervals it is also called geometric growth or geometric decay (the function values form a geometric progression).”

[6] See WHO, Media Centre, Ebola situation in Liberia: non-conventional interventions needed (September 8, 2014), available at http://www.who.int/mediacentre/news/ebola/8-september-2014/en/  See also NBC News, Fox, Ebola Spreading ‘Exponentially’ as Patients Seek Beds in Liberia (September 8, 2014), available at http://www.nbcnews.com/storyline/ebola-virus-outbreak/ebola-spreading-exponentially-patients-seek-beds-liberia-n198516

[7] See WHO, Media Centre, Ebola situation in Liberia: non-conventional interventions needed (September 8, 2014), available at http://www.who.int/mediacentre/news/ebola/8-september-2014/en/ : “As WHO Director-General Dr Margaret Chan told agencies and officials last week in New York City and Washington, DC, development partners need to prepare for an “exponential increase” in Ebola cases in countries currently experiencing intense virus transmission.”

[8] See CBS News, CDC director warns Ebola outbreak is “spiraling upward” (September 2, 2014) at http://www.cbsnews.com/videos/cdc-director-warns-ebola-outbreak-is-spiraling-upward/

[9] See Genetic Surveillance, referenced in n. 1.

[10] See WHO, Media centre, Ebola situation in Liberia: non-conventional interventions needed (8 September 2014), available at http://www.who.int/mediacentre/news/ebola/8-september-2014/en/  :“According to a WHO staff member who has been in Liberia for the past several weeks, motorbike-taxis and regular taxis are a hot source of potential Ebola virus transmission, as these vehicles are not disinfected at all, much less before new passengers are taken on board.”

[11] See BBC News Africa, Sierra Leone declares Ebola lockdown (September 6. 2014), available at   http://www.bbc.com/news/world-africa-29093048

[12] See HHS, CDC, National Center for Emerging Zoonotic Infectious Diseases, Ebola Hemorrhagic Fever Information Packet (2009) at p. 2 of 12. The document is available as a pdf download from HHS. You can find it at http://www.cdc.gov/vhf/ebola/pdf/fact-sheet.pdf . (Henceforth we’ll cite it as Information Packet at __.) There are, of course, later versions.

[13] See The New York Times, Opinion Pages, Osterholm, What We’re Afraid to Say About Ebola (September 11, 2014), available at  http://www.nytimes.com/2014/09/12/opinion/what-were-afraid-to-say-about-ebola.html?emc=edit_tnt_20140911&nlid=745484&tntemail0=y&_r=2

[14] Id.