Math Just Is

bad-math-teacher_med

FrozenPatriot sends this remediation for those (like me) who stopped learning when the maff got hard:

A long time ago, in an ancient land, there lived a very wise man who was the Vizier in the court of a great Sultan.

Many prosperous years passed and the great Sultan died leaving his young son, the prince, heir to the throne. Lacking both wisdom and experience, the prince started spending like a fool. Thus, the wise Vizier decided to teach the brash prince a lesson.

The Vizier convinced the prince to hold a great contest of wits for any who would enter. As a reward, the prince decided to give the winner whatever he asked, boasting of his great wealth and being under the illusion that it was essentially endless. Naturally, the Vizier won the contest and asked the prince for his prize: a single grain of wheat to place on his chessboard.

“What?! Just a grain of wheat! Are you insulting my wealth?”, scorned the prince.

“Certainly not, your majesty!” the Vizier exclaimed. “I am not yet finished. I also wish to receive double the amount of wheat each day until each square of the chessboard is satisfied, so on the first day you give me one grain of wheat on the first square, on the second day you double it on the second square (giving me two grains), on the third, you double it again on the third square (giving me four grains), and so on, until the chessboard is filled.”

“I thought you were so wise,” the young prince scoffed, “and that you would ask for something more substantial. Regardless, if this is your wish, you shall have it.”

So on that day the Vizier received his first prize — a single grain of wheat. On the second day he received 2 grains, on the third 4 grains, and the young prince couldn’t help himself making fun of the Vizier.

On the sixth day, the Vizier received 32 grains of wheat. On the eighth day — the end of the first row — he received a mere 128 grains. On the sixteenth day — the end of the second row and 25% through the progression — his reward was 32,768 grains. (2-3 bushels)

Less than nine weeks later, how many grains had the Vizier received?

The prince could not satisfy the reward because there’s not enough wheat on earth — 18,446,744,073,709,551,615 (18.4 quintillion or 18.4 million-trillion) grains!

Strikingly, this much wheat would cover all the land on earth to a depth of over 14 inches!

Study the number progression in this table (posted on WRSA’s dropbox for brevity).

That’s the power of exponential growth. The graph of the first two rows of the chessboard (16 spaces) looks like this:

image

The x-axis (along the bottom) shows the day and the y-axis (along the left) shows number of kernels of wheat. The top right point accounts for 2-3 bushels on the 16th day.

Because the last couple points dwarf the first few so severely, it’s helpful to look at the graph with a logarithmic scale on the left side (y-axis), like this:

image-1

As you can see by studying the the y-axis, the scale changes as you go higher. Logarithmic scales are useful for showing small and large numbers on the same chart. Because time is easily understood in linear terms, we will not change the x-axis to logarithmic.

Now, let’s add an exponential trend line to the first chart:

image-2

The black line shows typical exponential growth. Note that R2 = 1 above. This means the data points all fit perfectly along the line (1.0 = 100% accuracy). Anything less than 1 indicates the data doesn’t perfectly fit the line, but real-world data usually isn’t perfect.

Now, look at the same line on a log scale:

image-3

The black line becomes straight!

What’s my point?

Straight lines on log scales mean exponential growth.

Now, let’s look at some real-world data:

image-4

The blue dots are real data points (the top right point was recorded Monday, October 27th), and the black line is an exponential approximation of the data. In this case, R2 = 0.9748 (or 97.48% accurate) which is quite good. Let’s look at the same data with a log scale:

image-5

The blue dots follow the straight black line quite well, yes? This indicates the data is following a trend of exponential growth.

The real-world data presented in the two graphs above are, of course, the official number of world-wide Ebola cases, according to the World Health Organization (WHO). The x-axis (along the bottom) is the number of days since the outbreak began last March. As of today, October 31st, it’s around 15,000 and reliably doubling roughly every three weeks. As most of us know, the WHO freely admits their official numbers are low (due to misdiagnosing, not reporting cases, death before tests can be run, etc.) and that the actual total is 2.5 – 3 times higher — i.e. 35,000 – 45,000 cases today.

Am I saying this trend will continue forever? Of course not — but only because I’ve temporarily misplaced my crystal ball… Granted, there are differences between the West and West Africa – namely that we don’t kiss dead bodies during days-long funerals (Ebola concentration increases for several days after death and the dead are currently among the most common sources of new cases). In addition, most of us probably wouldn’t stone to death and dispose in septic tanks the bodies of aid workers who come to help us (which happened), although if we find ourselves at the point which aid workers need to venture to FUSA to stop Ebola, who’s going to come? …and how and why would they get to your neighborhood?

All that being said, clearly nothing has slowed it down so far.

If you’re curious what this trend looks like when projected into the future, here it is.

Disclaimer: past performance does not guarantee future results.

Also, please don’t let this influence your 2016 Independence Day party planning. Yet.

Ebola log graph

This is the same data set as above, with the trend line extending to an intersection with earth’s population. To those who say projecting (extrapolating) this data is meaningless, I largely agree and would have granted you the same in July with 1000 cases, while discussing extrapolating to 15,000 cases by Halloween. (RUBBISH, say you!) That said, the trend line extension above is still purely an exercise in curiosity.

As with physics, economics, and chemistry, math just is. Math does not have an agenda. Math does not vary with political whims or income levels or normalcy bias. If you disagree with the mathematical analysis above (except for the extrapolation), please don’t shoot the messenger or dismiss it.

If you disagree, simply prove the information above wrong using math, because that’s how math is disproved.

If you don’t believe that established trends generally tend to continue, give your written reasons below as to why not?

Be specific and show your work.

What external force will change this trajectory?

Perhaps you’ve located my crystal ball and can inquire in my absence. Are Westerners somehow different?

“It’s never happened before, so it just can’t!”

Very science-y. You might have a future as a globull warmist.

American healthcare is the best in the world?

I agree that it is. However it’s been finely honed for car crashes and chainsaw accidents and heart attacks, not 8-21 day viral hemorrhagic fevers with R0=2 and CFR=0.7.

Aesop and Doc Grouch have done outstanding work explaining this and I thank and commend them to the highest degree for spending their time freely contributing within their sweet spot. CA (our gracious host) has also given selflessly within his sweet spot, as have countless others within theirs, all of them deserving our laud and thanks (each of you has mine).

I happen to understand applied math (BS and MS in Electrical Engineering), and I’m willing to come forth from the among the readership and contribute where I can. I’m not telling you what to do, or how to plan, or when to act — I’m just presenting the math, and the math just is.

Venturing outside what I know and can prove, I HOPE the above extrapolation is wrong (who among us doesn’t?), that this just burns itself out, and that I can go on living life with my family without another thing to consider and for which to plan.

However — as most WRSA regulars already know — hope is not a strategy.

FrozenPatriot out.

52 responses to “Math Just Is

  1. Good work, geometric progression may indeed exist in Africa.

    When dealing with real biological systems you will often find the geometric straight line on the log scale curving down after w while as the presence of the progression itself (regardless of what it is, using up glucose , or an infection) changes the parameters and therefore the math involved.
    The math is tied to the RO which are a function not just of the agent but the environmental conditions it interacts with…Conditions change and they do affect the RO significantly. The RO numbers WILL change for certain if the pathogen leaves the current environment ( ie goes to Europe or US) and so the underlying math changes.
    That how it is in biological systems. the progression itself changes the environment it is in

    I hope for the reset as much as the next guy and am willing to take it in nearly any form.
    But short a significant mutation (and we are ALWAYS just one mutation of the FLu away from a reset) EBOV isnt it (yet).

  2. The overall trend numbers could remain the same, but there are some data points we need to consider. For example Ebola is running fast and hot in west Africa right now.

    Individual locations and countries will spell different results. By that I would project we will start seeing oscillations as the outbreak spreads.

    For example: Ebola lands in Singapore with one or even 10 cases. The exponential growth chart has to restart all over again. Same as when it arrives in a new region or population of people.

    Before you start shouting “But the air planes! The ships!” Yes what about the airplanes and ships?

    It does not matter yet at this stage in the game. The spread out of west Africa so far is in the ones and twos. So the starting number in each new region is again tiny and has to rebuild from zero.

    The overall growth rate has to oscillate the bigger it gets. Like a sine wave. The fact that the sine wave is still going up bodes ill for everybody, but will give others a chance to live just a little bit longer. Until the economic disruptions start happening.

    For example the Philippines is dependent on many things for import. Plastic, fuel, wheat, metal etc. But it is a isolated island archipelago geographically. What if the authorities there decided to shut down the ships and planes and damned the consequences? There is 90 million people who will not die of Ebola but who will die cause the Indonesian coal that powers their power plants will stop coming.

    Other things like economic disruptions will slow or stop the spread of this higher in the progression of the spread, even odd pockets of Ebola free areas will form.

    The growth of this is like gravity, but even gravity can be expressed as a wave.

  3. But just how much will that change when it hits any of the hives in the US? Or do you see the typical hive dweller as being THAT far removed from where Ebola currently runs rampant???

  4. Alfred E. Neuman

    Reblogged this on The Lynler Report.

  5. Bravo, F.P.
    Streamers and balloons.

    If you could do that 5 minute briefing for the heads of the major networks and newspapers, it couldn’t help but have an effect.

    If somebody did for their congressfool, it might even have an auspicious effect. At least on bringing 3000 troops home who’re being staked out like a goat for a pack of lions.

    Unfortunately, the people at CDC who should grasp this have been busy telling us to “pay no attention to the man with the chalkboard talk”, because their boss the idiot savant has an urgent tee time, and “Raaaaaaycissssssss!”

    And I’m linking this little presentation myself.
    Thanks for the effort.

  6. Consider away, B Metz. And choose whatever you wish, to matter to you.

    That’s Rightful Liberty. Ain’t a chance in the world that anything else could save us now. At least the thinking part is over…socially speaking, anyway.

  7. If this tyranny shit doesn’t get stopped, and quick, I don’t think it’ll matter if ebola gets spread or not. Details…if it ain’t this, it’ll be that.

  8. Aesop and Doc Grouch have most likely covered the aspect of the pandemic in their discussions, but this is still a good story because it once again proves the .gov is lying, and because of the longer “shelf life” of the disease.
    http://www.zerohedge.com/news/2014-10-31/story-changes-ebola-now-aerostable-and-can-remain-surfaces-50-days

    Now there’s a woman in the Portland OR area being monitored.
    http://www.katu.com/news/local/Person-monitored-for-Ebola-hospitalized-health-officials-say-281124492.html

  9. There are 3 types of people in this world. Those that understand math, and those that do not.

  10. Yup.

    I’ve referred to the Canadian Public Health Agency’s MSDS for Ebola so often in the last month on the 50 days thing I have it permalinked on my toolbar:
    http://www.phac-aspc.gc.ca/lab-bio/res/psds-ftss/ebola-eng.php
    “Section IV: Survival Outside Host” is the highlight, along with methods of inactivation of virus.

  11. The exponential-like curve is the left half of the logistic curve. If your trend still looks exponential you’re still in the left half, and you can predict the right half will arrive:

    https://en.wikipedia.org/wiki/Logistic_function

  12. Again, the numbers, calculated in March and effectively matching since then:

    Mar, 2014 – Infected: 104 Dead: 62
    Apr, 2014 – Infected: 194 Dead: 116
    May, 2014 – Infected: 360 Dead: 216
    Jun, 2014 – Infected: 670 Dead: 402
    Jul, 2014 – Infected: 1,247 Dead: 748
    Aug, 2014 – Infected: 2,319 Dead: 1,391
    Sep, 2014 – Infected: 4,313 Dead: 2,588
    Oct, 2014 – Infected: 8,022 Dead: 4,813
    Nov, 2014 – Infected: 14,921 Dead: 8,953
    Dec, 2014 – Infected: 27,753 Dead: 16,652
    Jan, 2015 – Infected: 51,621 Dead: 30,973
    Feb, 2015 – Infected: 96,016 Dead: 57,610
    Mar, 2015 – Infected: 178,590 Dead: 107,154
    Apr, 2015 – Infected: 332,177 Dead: 199,306
    May, 2015 – Infected: 617,849 Dead: 370,709
    Jun, 2015 – Infected: 1,149,199 Dead: 689,519
    Jul, 2015 – Infected: 2,137,510 Dead: 1,282,506
    Aug, 2015 – Infected: 3,975,768 Dead: 2,385,461
    Sep, 2015 – Infected: 7,394,928 Dead: 4,436,957
    Oct, 2015 – Infected: 13,754,567 Dead: 8,252,740
    Nov, 2015 – Infected: 25,583,494 Dead: 15,350,096
    Dec, 2015 – Infected: 47,585,299 Dead: 28,551,179
    Jan, 2016 – Infected: 88,508,656 Dead: 53,105,193
    Feb, 2016 – Infected: 164,626,099 Dead: 98,775,660
    Mar, 2016 – Infected: 306,204,545 Dead: 183,722,727
    Apr, 2016 – Infected: 569,540,453 Dead: 341,724,272
    May, 2016 – Infected: 1,059,345,243 Dead: 635,607,146
    Jun, 2016 – Infected: 1,970,382,153 Dead: 1,182,229,292
    Jul, 2016 – Infected: 3,664,910,804 Dead: 2,198,946,482
    Aug, 2016 – Infected: 6,816,734,096 Dead: 4,090,040,457

    Sand in the hand.

  13. But…but…science! Lab coat! Protocols!

  14. Math doesn’t lie. That is true. However, it is important to remember that math is merely a tool that we humans use to describe natural phenomenon. In this case, you are attempting to use math to describe the complex interaction of a parasite, its host, and the hosts to each other and to society in general.
    The first thing to consider is biology: Any community of organisms reaches a stable state with respect to its environment and its population. This is called “carrying capacity.” The carrying capacity of a biological species in an environment is the maximum population size of the species that the environment can sustain indefinitely, given the food, habitat, water and other necessities available in the environment.
    In other words, there are factors that affect the population size of any species, and this includes the Ebola virus. Eventually, there will be factors that limit the exponential growth of the species. The climate of the host country, population density, and even the behavior of the host will limit the growth of the population.
    For example, once Ebola runs wild in the West, the people there will panic. So football games, school, or other large gatherings, either by government edict or be spontaneous consent. Sanitation, social interaction, all of that plays into the spread of the disease.
    I think Ebola will get MUCH worse before it gets better, but I predict that the pandemic will peter out long before it kills of the human species. How bad it will be is anyone’s guess: ten million deaths? 100 million? Who knows?

  15. Jimmy The Saint

    Of course, that progression requires increasing contact with fresh folks to infect. At some point, the potential new victims become too remote to infect. Headhunters in New Guinea probably won’t become exposed, for example.

  16. Before I retired I was a professional technological forecaster. I often used exponential curves for forecasting some technological capability. However, for forecasting the rate at which some technology would “take over” an entire market, I found Logistic curves were better tools. The same should be true here. As the fraction of the population infected with Ebola (or any other disease) grows, the fraction left to become infected (obviously) shrinks. The differential equation for rate of growth of the infected population will look someting like this:
    rate=(#infected)*(#not yet infected)*(growth constant)/(total population). When integrated, this differential equation becomes a Logistic or growth curve. The “growth constant” may not actually be constant, if measures such as quarantines are established, but this gives the general idea. Early on in the epidemic, the ratio of (#not yet infected) to (total population) is only slightly less than one, so the logistic and an exponential are very close until a significant fraction of the population is infected, at which point the rate of growth slows down. Thus your exponential fit to the early data is to be expected.

  17. Interesting stats in this piece — http://www.washingtonpost.com/news/to-your-health/wp/2014/09/11/ebola-is-devouring-everything-in-its-path-could-it-lead-to-liberias-collapse/

    Sorry but I will go into the same argument that I had with Aesop, from a epidemiological point of view something like Ebola or any disease is not a true doubling if there are deaths involved. Lets go back to the chessboard example. Lets say by turn 3, Vizier decides to eat a grain of wheat. The next doubling is six not 8. Then on the next turn Vizier eats 2 grains, so the next doubling is only 8, not 12, and so on thru the progression. To have a true doubling you don’t eat any of the wheat or have any deaths. Its the more honest appraisal of your presentation. Any solace in the outcome? Nope. It would merely delay final outcome by 2 turns at best.

    Here is an example of death curve for the Black Death in Florence for the period — http://pcwww.liv.ac.uk/epidemics/Hist_image_florence_1400.htm
    Infection curve in Switzerland for the Spanish Flu of the period — https://c1.staticflickr.com/1/33/64609577_dfeaa5c9ec.jpg
    Commonality? A point is reached where the doubling collapses for lack of resources.

    My point is this, no disease follows a log rate death curve. The disease abandons that curve early in the pattern for the simple fact that at some point the locale is no longer a target rich environment for infection. Not much comfort with all the corpses lying around. But since this is a theoretical exercise anyway, please lets impute all the factors.

  18. Great, great stuff. Thanks. No matter what happens with ebola, we know this much for sure…it’s either Rightful Liberty or it ain’t.

  19. Yes, at some point the numbers will fall off the absolute log line.
    But at that point, we’ll be talking about tens to hundreds of millions, unless someone finds a way to break this disease’s back.

    Africa is a target-rich environment of 1.1B potential infectees.
    Asia is 4B more.
    Health care in both places is largely a fairytale, and the majority of those populations live in teeming slums.
    And when either or both is 20-30% involved, even the West will be in flames, because we’ve got the same idiot underclass here with no more common sense than tribal villagers.
    And the problem is, the people there are just smart enough to do the things that will spread the disease beyond its current border: they’ll try to get out, and bring it with them.
    This thing has the potential to kill, in one year, more people than all wars since we started tallying the details on clay tablets.

    The only good news about it is that a lot of people here have the opportunity to plan ahead and so arrange their lives such that they won’t be in the future contagion pool, thus avoiding those particular consequences.

    But that it won’t wipe humanity out down to the last person won’t be very comforting at that point, and when the disease begets interruptions in supply chains, power generation and energy delivery, it’s the 18th century again in most places.

    Then you’re looking at famine, from local to continental.
    West Africa knows already that they’ll be there next year because of what’s already happened. Malnutrition lowers disease resistance; eventually it also kills people.
    Then the other diseases get their turn: cholera, typhus, etc.

    Coupled with any number of countries that might take the opportunity to settle a score or two, once adult supervision is otherwise engaged, this is quite enough to have to deal with, long before we get to the last few doublings on the line.

    Even a bomb falling toward your head isn’t a big deal, if you see it coming, and can move far enough away in time. The problem is the people who were supposed to watch weren’t paying attention, and now we all may not be able to get out of the impact area before we get tagged.

  20. Hat tip to you, good sir. Very clear, lucid, and disturbing.

  21. Dick Summers

    You forgot ‘Pocket Protector’.

  22. Mark Waechter

    Dang it! Good bourbon came out my nose.

  23. Disclaimer: Not a rocket scientist nor did I stay at a Holiday Inn.

    But, if the target rich environment dries up in West Africa/All of Africa, does the progression slow (speed bump) / momentary pause or does the progression take into account they’ve exported to other areas of the world for continued growth? Also, not building us up to be this great 1st world panacea but does progression not slow since we don’t eat bats or crap in the street? Or is that method of transmission no longer a requirement, person to person is all that’s needed going forward in FUSA?

    All this postulating is great, but can we come up with a plan(s) with all these great minds floating about in the patriot community? Meaning, when do I need to get the hell out of dodge? 1 case in 5 miles? Don’t want to quit the job and rip the kids out of school too soon you know.

  24. Watch Al Bartletts exponential growth and you will have a little better understanding of when you need to get out…

  25. Frog, Lineman’s suggestion is good, though you didn’t need me to type that. 😉 I’d suggest 1 case in 20 miles, but it’s only a suggestion, I can’t and won’t tell you what to do to protect your family. I’d also suggest not focusing only on the pandemic, read the link, there’s a lot going on.

    http://thelibertysphere.blogspot.com/2014/11/danger-of-civil-war-places-conn-on.html

  26. NightWatcher

    IIRC, Aesop made the claim pretty clearly that nobody (at least with any sense) believes that the logarithmic growth continues “forever” it is simply a reductio-ad-absurdum argument to show the power of logarithmic growth.

    As to the point where logarithmic converts to logistic, it is anyone’s guess. You can’t even begin to estimate until you see some (however slight) reduction in the rate of growth, at which point you can make a WAG.

    From an engineering perspective, you may be able to put some limits on when the host availability is limiting. There appears to be some flattening of the rate in Liberia (whether this is real or artifact remains unclear), and the current penetration is approx. 6500 cases out of a population of 4 million, or approximately 0.16%. Even with an optimistic fatality rate in the FUSA of 10%, this would equate to ~53,000 deaths before the rate starts to decrease. We might consider this a “lower limit”.

    This is why it is critical that we prevent any cluster formation. And the best way to prevent this is to stop importing the damn thing. It is exactly this continued “salting” of “isolated cases” which will lead to a cluster.

  27. NightWatcher

    Addendum:

    I have to assume TPTB are well aware of these facts (thank you Sun Tzu).

    At what point do you think the bleating sheep demand that Uncle Sugar protect them, by any means necessary, from this scourge. When will Uncle Sugar “reluctantly” and with “an over-abundance of caution” relent and provide them the “protection” demanded. At that point, what will they be willing to give up, for a little security.

    Anything?
    Everything?

  28. There are 10 types of people in the world.
    Those who understand binary and those who don’t.

  29. The disease doesn’t care where it grows. If you have 1 country making 200 cases a day, or 50 clusters in 10 countries only making 4 cases@/per day, the result in each case is 200 new cases a day. Note that it still doubled in Dallas despite hazmat gear. They stopped it at Generation Two, but it still doubled in 21 days right here despite best efforts.
    BTW, there’s no reason to think it’s slowing down whatsoever in Liberia; any numerical slowdown in the posted figures is entirely attributable, at this point, to crappy accounting/lying, not an actual lack of new cases. And there are 1M people in just Monrovia, so 6500 cases countrywide hasn’t even put a dent in that. There are still, even using the crappy numbers, 6K-7K more new Ebola patients walking around than there are beds to isolate and treat them in the region. So imagine 2000+ Thomas Duncans wandering around Dallas-Ft. Worth, 2000+ in El Paso, and 2000+ more in greater Texas, and tell me you seriously think the infection spread is or would be decreasing.

    The fact that we don’t eat bats or kiss dead people cuts out those initial vectors. But kids still stick their fingers into everything, then their mouths, then get kissed by mom and dad, then get taken to day care, lather/rinse/repeat. Flus season starts every year along with school season, kicks into high gear from Thanksgiving to Easter – because multi-generational feasts, kids, food, and too cold to go outside – and it only goes away when long, warm days get people out on the sunshine, and swimming at the pool, lake, or beach, which washes their nasty bodies much better than a 15 minute shower, or 30 seconds at the sink. {Poof!} No more flu season. Every year.

    As far as when to go, that’s individual decision-making.
    First off, have a place you can go.
    (I’m assuming everyone knows that “to the forest/hills” ain’t a plan, and we’re about to start 4-5 months of what promises to be a severe winter.)
    Second, have a local fall-back in case you end up not being able to get there.
    (Bug in vs. bug out, right?)
    Third, be able to sustain yourself either place/way.
    Only then would I worry about the when. Mull it over, but come up with a line that’s your personal “go” limit. (Somebody up the street/at work/at the kids’ school is confirmed infected. Or random cases are popping up all over in town. Zombie hordes of walkers are shuffling down the main street. Whatever.) You could always burn a sick day, bail out, and then re-evaluate from there once you’re safely out. But the key is still ,Rawles suggestion: “Better a day early than 5 minutes too late.” Because if the next county or governor puts up barricades, unless you have a personal helicopter on the roof, you’re done.
    {Consider changing your DL address, and car reg./tags/plates to where you want to bug too, because you’re far likelier to be allowed to go “home” then be allowed to get let “out”, in that event.}

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  31. FrozenPatriot

    I agree that oscillations are typical in cases like this, and that we’re all trying to predict the future — but only by educated guesses, and that other factors (ecinomical? geopolitical?) will come into play, however I can’t swallow that gravity is sinusoidal.

    Force of gravity (N) = mass1(kg) x mass2(kg) x gravitational constant (6.67384 × 10^-11 m^3 / ( kg * s^2 )) / distance(m)^2

    …nothing sinusoidal there…

  32. FrozenPatriot

    Thank you, Aesop. And thank you for your considerable efforts too. This little math class pales in comparison to 3-5 posts a day for weeks…

    I mentioned to CA in an email, but I should mention it here too, that I will be updating the historical and projection graphs as new WHO data becomes available. The graph that spurred this post will remain at http://bit.ly/1wGbp6S and will be updated. I’ll add the graph of historical data (with trend line) for those who prefer not to observe the extrapolative projection.

  33. FrozenPatriot

    You beat me to it… 🙂

  34. FrozenPatriot

    Agreed on all counts, and I hope (there’s that word again…) you’re right about the pandemic ending before thoroughly circling the globe. On that note, I don’t believe it can kill off the human race, as CFR<1 and survivors apparently can't catch it again.

    Please allow me to restate my disclaimer: "past performance does not guarantee future results." I was merely making the observation that the historical data is trending exponentially.

  35. FrozenPatriot

    Thank you for that, Joseph — it makes perfect sense. I don’t believe that the end game is billions of new cases a week, infecting every person on the planet. Nor do I believe the data will follow the projection above much longer. While I still can’t find my crystal ball, I’d bet this thing goes asymptotic (different than asymptomatic) to vertical for a while as figures are updated to account for previously unreported cases, and hordes of new hosts are offered up on silver platters by Marxists acting under the guise of political correctness and globalism.

  36. I am not a scientist, but I have two observations to add to this discussion. First, tell the American Chestnut that the blight will “burn out” before they all die of it. Crap. We can’t because they all died. Second. I read somewhere online about the genetic rate of change for the current Ebola outbreak is on the same time line as seasonal flu. Meaning. 12 to 18 months from now, survivors of the first round will now be susceptible AGAIN to the new strain. Just like you can get the flu over and over again. Just without a 70% death rate. So the world doesn’t need a vaccine to save it from Ebola. The world needs A NEW VACCINE every 12 months to save it from Ebola. OK, so let me add a third observation. At some point, not too far down the time line, the global economy is going to fall apart, as the global “just in time” system falls apart. And anything that disrupts the “just in time” food production and distribution system will accelerate the process. Then let’s mix in social disruption in the United States because the 50% of the population that gets everything from a government check, even social security for retirees, suddenly has no buying power, or even no check. I live in the rural country. Here is an observation. If I take a house dog, and release it in the wild to fend for itself. It will show up on a neighbors front porch 3 months from now, starved, sick, and DESPERATE. So even though a wild coyote can fend for itself in the exact same environment, the released house pet WILL DIE. May I suggest that most people in the developed world are house pets that will suffer the same fate as a released house dog once the “just in time” systems begin to fall apart. Long before everyone is sick with Ebola. Just thoughts.

  37. NightWatcher,
    If Ebola follows the pattern of the Spanish Flu it will actually accelerate along the log line as this article points out then summarily collapse. Go take a look at the graphs I posted earlier. The discomforting factor is that folks back then knew the pathology of what they were facing, we don’t. And worse we don’t seem to care to find out.

  38. NightWatcher

    Which is why I precisely DIDN’T make any assumption on the upper limit, because to do this would be be a WAG.

    My assumptions were very clear:
    1) We can expect a similar penetrance into the population without seeing any significant decline in R0. Granted a weak assumption, but at least there is some historical data (not a WAG).
    2) The mortality rate will see a half-log reduction. As stated, an OPTIMISTIC assumption.

    Point being, even with this conservative lower limit, half a million infected and 50K dead, you can kiss the health-care system in the FUSA goodbye.

    Leviathan’s response will kill many more.

  39. Math doesn’t lie … but the CDC does. One: we have no actual knowledge of how many people are sick from ebola and how many may have died from it. Propaganda is rampant. The tests, when made, are not reliable and egregiously misrepresented to pump up vaccine sales. Two: those who are most susceptible to this virus generally have highly depressed immune systems. Three: The DOD studies proved high grade colloidal silver killed ebola and other similar viruses in vitro. So…. Four: get yourself some high grade colloidal silver and start dosing. If you get ebola, increase the dose until you are well… or dead. Good luck.

  40. Citations, please:

    …The DOD studies proved high grade colloidal silver killed ebola and other similar viruses in vitro…

  41. A point to consider, that the transmission rate (new persons infected/already infected victim) would vary between populations. The populations in Africa now at the heart of the epidemic may have a higher transmission rate than elsewhere. While the disease grows out of control on one area, and sporadically infects pockets elsewhere, unless those outside areas have a transmission rate > 1 those pockets will fade out.

  42. lucius.cornelius

    You fell into the same trap that the young ruler did. You take limited knowledge (no awareness of the veracity of the figures you use or acknowledgement that ‘exponential growth’ requires unfettered access to the growth medium) and seek to apply it to a continent.

  43. Pingback: Ebola and Math Is | stoshwolfen

  44. The man who first diagnosed Ebola noted that it (like HIV) is not a very effective parasite. Provided people are educated as to the dangers of Ebola and how it’s transmitted, these numbers will remain just that. Numbers. Probably the best way to contain Ebola is to go to west Africa and educate and help people. Anyone?

  45. NightWatcher

    Another newsflash, dilute chlorine solution kills Ebola in vitro. Hell, soapy water (give or take some harsh language) kills Ebola in vitro.

    Given that any virus can only replicate inside of a host cell, I’m not really interested in what is does on glass (in vitro). How about in vivo?

  46. NightWatcher

    Try giving that advice to the folks who turned up in the village septic tank.

  47. FrozenPatriot

    Thanks, Doc, and right back at ya for your fine work too…

  48. FrozenPatriot

    I merely charted actual data and observed a trend correlating to exponential growth. The projected trend line was purely an exercise in curiosity and I make no claim to its veracity. You may have missed my disclaimer: “Past performance does not guarantee future results”.

  49. FrozenPatriot

    …so WHO issued new numbers Friday and I just now got a chance to add them to the running total and graph. (I’m traveling last weekend and this week with limited internet access on the ol’ laptop)

    http://bit.ly/1x2P70d

    The total cases went down by 136 between Wednesday and Friday of last week. According to the 31OCT WHO SITREP, “the cases reported are fewer than those reported in the Situation Report of 29 October, due mainly to suspected cases in Guinea being discarded.” Keep in mind this same crowd of assclowns readily admits a deficiency factor of between 2.5x and 3x.

    Why would they revise already-low numbers further down??

    Also, the total deaths went up by only 31. Don’t get me wrong — 31 dead people still sucks and I’m by no means cheering for more — however the 10 reports (roughly a month) preceding the last three averaged 225 deaths per reporting period. The last three reports have declared 46, -2, and 31 deaths respectively, for a total of 75. Compare this to more than 700 deaths which should have occurred, statistically speaking…

    This alleged drop in deaths also knocked the CFR (Case Fatality Rate) from between 50% (the 20OCT SITREP) and 58.5% (the average of all SITREPS) down to 36.5%!! This is largely due to Liberia’s numbers in the 25OCT and 27OCT reports. Liberian cases jumped from 4665 up to 6535, however deaths decreased from 2705 down to 2413, causing Liberia’s CFR to drop from 58% down to 37%…

    The cynic in me wants to believe the WHO is padding the numbers lower still in order extinguish rekindled ridiculous, antiquated notions like individual preparedness, national borders, sovereignty, and common sense.

    Stupid slaves…thinking those things still apply…