Doubling Time and the Future

This is a simple posting about what the doubling time of a virus means for our future expectations.

We can expect a 3 week or so doubling of cases of Ebola until such time as we gain control of the spread or develop an effective cure. That may take a while. So what happens until that point? How much worry and how much time?

So lets just list a set of “doubles” and realize that it is about 3 weeks between each set. We had our first (not flown in by a medical air ambulance) patient in Dallas. Now a couple of weeks later, our first home grown transmission (to his nurse, despite medical protective gear). So that is our first “double”, from 1 to 2.

2  4  8  16  32  64  128  256  512  1K  (that '1k' is about 1000)

In weeks, that’s roughly 3 x 9 or 27. Call it about 1/2 a year. Just a while ago, Africa hit the 1000 patient mark, so we ought to expect that this all started about 1/2 a year ago. (Someone can test that if they like by looking up the index case and seeing how good the fit might be.) Now what happened after that 1000? Doubling continued. That same row can be repeated as 1000’s if desired.

2  4  8  16  32  64  128  256  512  1000x1000 (or One Million).

Now last news I heard had Africa at 4000 dead (and about 8000 infected). That puts them at about 3 x 12 weeks, or about 9 months into it. That is where we ought to be about next July… But where will THEY be by then? A whole lot worse. Now we can repeat that doubling as millions.

2 4 8 16 32 64 128 256 512 1000 Million (that Americans call Billions, and Brits don’t ;-)

OK, so the world ought to be about 12 steps on by then (next July). Counting from 8k now, we get about 32 Million. Doubling Time is a bitch…

For the USA, how long to that 256 (that is nearly the entire population)? As we are already at 2, counting forward is 9 to the end of the first line, then 10 on the next line, then another 8 on the last line. 27 x 3 weeks, or about 81 weeks. Call it 20 months, give or take, until everyone in the country is either exposed, sick, or dead. That is ALL the time you have to find ways to stop the transmission. One year, 8 months. With a wall around the country and no new imports.

Now the world as a whole is already at 8,000 so how long to, oh, 8 Billion? It is a 17 count to 1 Billion, then you repeat the line of doublings as Billions, and get another 3, So 20 x 3 weeks or 60 weeks. Call it about 15 months. One and 1/4 years. Tops.

Do I think that will happen? No.

Long before then folks will start stopping this disease. If not by modern medicine, by good old fashioned quarantines (that were used since they worked… without modern medicine). At some point air travel shuts down and lots of folks shelter in place and figure they will deal with the side effects of not going to work after they find out who is still alive….

But this exercise DOES put an upper bound on how long this can go without a fix. February of 2016, we run out of world to infect. This event will be measured in months, not years. That is the tyrany of doubling time. (Or exponential growth).

Again, though, I have to point out that before that actualy happens, the S curve nature of real growth will bite. We will run out of pilots willing to fly to infected places. We will run out of folks willing to congregate in airports (or factories, or…) and things will stop; even without a cure, fix, or change of “medical protocol”.

Me? I don’t plan to do anything different until we hit about 1000 patients in the USA. That’s about 1/2 a year out. Call it April 15, 2015 or so. A fitting date… That has odds of about 300,000 : 1 on me being too late, and those are OK odds with me. At that point, I cash a chunk of the 401K, buy an RV and a couple of acres out in the boonies, and pack my water purification kit, a load of bleach, and food; and go camping for a year or so…

I don’t expect that to happen, BTW. But it is nice to know when to start taking it seriously. IFF this isn’t ramping down / being quenched, by then, well…. That also lets you know how to evaluate the response of the WHO, CDC, and others. They have 6 months to get their shit together before the shit has hit the fan and you can’t get in front of it. That isn’t a lot of time. I hope they know how to figure doublings…

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About E.M.Smith

A technical managerial sort interested in things from Stonehenge to computer science. My present "hot buttons' are the mythology of Climate Change and ancient metrology; but things change...
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23 Responses to Doubling Time and the Future

  1. Sandy McClintock says:

    Months Number
    0 2
    0.7 4
    1.4 8
    2.1 16
    2.8 32
    3.4 64
    4.1 128
    4.8 256
    5.5 512
    6.2 1,024
    6.9 2,048
    7.6 4,096
    8.3 8,192
    9.0 16,384
    9.6 32,768
    10.3 65,536
    11.0 131,072
    11.7 262,144
    12.4 524,288
    13.1 1,048,576
    13.8 2,097,152
    14.5 4,194,304
    15.1 8,388,608
    15.8 16,777,216
    16.5 33,554,432

  2. Adrian Vance says:

    You have not accounted for the shrinking source or target population. This is not as simple a system as you have postulated. It requires two simultaneous equations.

  3. Simon Derricutt says:

    Maybe something else to figure in is that maybe someone working in a factory gets ill and infectious. I don’t know how long the virus stays alive and dangerous out of the body, but the various pictures of people spraying bleach around implies that it can survive some time. That factory’s produce could be exported and produce new centres of infection in other countries.

    Shades of “The Stand” anyone?

  4. Speed says:

    The current method for curtailing the spread of Ebola is diagnosis, quarantine, contact tracking and observation. I have seen no numbers on the personnel requirements for this but I suspect that without early control there could be a race to contain the disease before we run out of healthcare workers — and the facilities, equipment and supplies they need to do their jobs.

  5. philjourdan says:

    “quaranteens” – Quarant the teens? ;-) That will also cut down on teenage pregnancy.

    Doubling is a female dog. But nature will not be denied. PC has enabled the disease to spread. Eventually it will kill thousands here (because after the doubling stops, there are still infections and more people getting it, just not a doubling). The days of Sodom and Gomorrah are coming to an end. And it is all due to the stupidity of Obama and his minions. Typhoid Mary was not an innocent persecuted victim. She was quarantined because of the threat she posed.

  6. j ferguson says:

    Spouse’s grandmother moved mother and aunt to very small community in NW corner of NJ for the Spanish Flu epidemic in 1919. They stayed there for 6 months although mother, aged 99 now, isn’t certain. It worked for them.

  7. A C Osborn says:

    I have been arguing for months with warmists that ebola is far more dangerous than some possible minor increase in temps some 100 years in the future.
    The money that has been wasted on “AGW” could have been spent on much more productive and meaningfull things.
    Once the ebola virsu left the first village it was already too late to stop thousands dying because it did not burn out as it has in the past.

  8. R. Shearer says:

    Makes you wonder why we are not being more judicious about reducing or ending commercial travel out of Western Africa. In any case, we’ll get some advanced warning based on how it continues to spread in Africa and on to the Middle East, Europe and Asia which are closer and have more contact.

  9. Pouncer says:

    There is some study regarding typhus/typhoid that indicates the disease evolves. A disease that quickly and thoroughly incapacitates its host can’t spread far or fast (the impaired host is too weak to travel, and so is the disease). A disease that is only mildly inconvenient to the host spreads widely. (Colds spread because the infected refuse to stay home from work or school– or wear snot-catching masks.)

    When santitation measures (given typhus, we’re talking sewers) are poor, the disease spreads more easily, (as fecal matter in streets and gutters) so can remain incapatitating. When sanitation is rigorous, the disease evolves to a less incapacitating form, so that it can spread by a moving host rather than the host’s moving feces.

    Arguably the strains of HIV seen now are more survivable than those that afflicted our culture in the 1980s, for these sorts of reasons. If the habits that allows the virus to spread are less common, the disease itself must present later or less symptomatically. Our treatments may be less effective than we hope, while our behavior more important.

    So, too, the progress of Ebola may depend on our behavior rather than our tech. We’ll learn as we go.

  10. Speed says:

    j ferguson mentioned the Spanish Flu Epidemic. For those not familiar …

    The 1918 flu pandemic (January 1918 – December 1920) was an unusually deadly influenza pandemic, the first of the two pandemics involving H1N1 influenza virus. It infected 500 million people across the world, including remote Pacific islands and the Arctic, and killed 50 to 100 million of them—three to five percent of the world’s population—making it one of the deadliest natural disasters in human history.

    Most influenza outbreaks disproportionately kill juvenile, elderly, or already weakened patients; in contrast the 1918 pandemic predominantly killed previously healthy young adults.

    This is in no way intended to draw a parallel between the current Ebola epidemic (the CDC’s term) and the 1918 flu pandemic but j ferguson’s comment reminded me of my grandmother’s memories of that horrible tragedy. She was a young nurse working at Naval Station Great Lakes at that time. She told of coming to work each day and seeing that many of the patients she had nursed the day before were gone. Dead. She described the stacks bodies in words similar to what I have read about the US Civil War. But there was/is a difference between the flu and Ebola. My grandmother survived the pandemic even though there was no 21st century high tech protective gear. Not everyone exposed or infected died.

    The concern today is (or should be) that areas with poor health care infrastructure or inadequate response will suffer massive (a word I hate and almost never use) deaths along with and/or followed by economic collapse.

    By 10 October, 8,376 suspected cases and 4,024 deaths had been reported; however, the World Health Organization has said that these numbers may be vastly underestimated. The WHO reports that more than 216 healthcare workers are among the dead, partly due to the lack of equipment and long hours.

    4,024/8376 = 48%. This is bad. Very very bad.

  11. E.M.Smith says:

    @Adrian: That happens at the point where the S curve inflects from exponontial upward to rounding over. At about 4 Billon sick and dying. Not real relevant as the other half are pretty much guaranteed exposed by then…

    @Simon: Dry survival is reputed to be short. Hours or less. We will see…

    @Speed: With 10 to 100 contacts to trace per patient and hours to trace vs seconds to spread, we are alredy in The Red Queens Race…

    @J Ferguson: Also worked during the Black Death. Folks in closed rural estates lived.
    Boat ought to work too.

    @Pouncer: Diseases all tend to evolve from lethal toward parasitism… unless … they are mostly resident in some other species. Then our mortality is not selective. Ebola is predominantly selected for the non human reservoir species. It might evolve a human form though. Some folks do become asymptomatic carriers, though rare. Not clear if they eventually clear the virus. The worst risk is that it can reservoir in something like rats or squirrels, then become endemic while staying lethal to us.

  12. Sandy McClintock says:

    Did you see a possible ‘Ebola treatment’

  13. Speed says:

    From today’s Wall Street Journal …

    Congo has years of experience fighting this disease: It has world-class Ebola experts who have responded to countless outbreaks, as well as multiple, national-level laboratories that are devoted to the diagnosis of viruses. When people in Congo began falling ill this summer, local labs within a week were able to determine both that Ebola was the cause and that the virus was distinct from the West African epidemic. The Congolese response included immediate site visits and the deployment of a mobile lab for on-site diagnostics, reducing response time, and the effective isolation of Ebola cases.

    More to the point of this discussion …

    Today, the length of time needed for foreign aid to reach its destination, as well as the ability of countries to rapidly and effectively use assistance, pose real problems in need of solutions.

    Clearly the currently uncontrolled Ebola outbreak can be viewed as the failure of government to fulfill one of its primary responsibilities — public safety.

    The author of the above WSJ text is Nathan Wolfe “the founder and CEO of Metabiota, which develops systems for monitoring and managing disease spread.” He has a horse in this race. But he also has useful knowledge.

  14. Power Grab says:

    I have an ancestor who was a country doctor during the Spanish Flu epidemic. He treated more than 70 patients for it and didn’t lose any of them.

  15. j ferguson says:

    Hi Speed,
    It’s probably a bit off topic, but a great aunt of mine was a nurse at Presbyterian Hospital in Chicago from around 1900 to the late twenties. She used to tell us kids stories of the Chicago Fire and I had always supposed she had been at the hospital at the time, but my mother reminded us that she wasn’t old enough and that what we were hearing was stories from the other nurses who had been there at the time of the fire. I think she thought the fire stories more interesting although she did mention the flu.

    It’s too bad that some of us didn’t recognize the value of what our elders have to say when they are still around to share it.

  16. tom0mason says:

    Some of the stories nationally and internationally on the Ebola crisis in Africa and at home.

    Nurses in US, Britain, Canada, and Spain have highlighted the lack of protective equipment when caring for Ebola cases.
    Via ReliefWeb, a report from the Assessment Capacities Project: ACAPS Briefing Note: Ebola in West Africa: Impact on Protection and Security – 14 October 2014. Click through to download the PDF.
    The summary and then a comment:

    This publication is in two parts: it begins with the impact of the Ebola outbreak on Protection and then provides an update on the progress of the epidemic since the previous briefing note, published on 25 September.

    Crisis Overview
    • UN and national officials are warning of the serious threat Ebola is posing to the safety of the countries.
    • The Governments’ poor management of the epidemic …has exposed citizens’ lack of trust in their governments and exacerbated social tensions, increasing the possibility of profound unrest in these fragile countries. The lack of a prompt, robust, and efficient response from the international community contributes to the mistrust.
    • Children and women have been deeply affected by the EVD outbreak. Children related to people with EVD have been abandoned. Children are extremely vulnerable and in critical situations in the three most-affected countries due to the loss of a parent.

    – At least 3,700 children in Guinea, Liberia and Sierra Leone have lost one or both parents to Ebola since the start of the outbreak in West Africa and many are being rejected by their surviving relatives for fear of infection. Humanitarian constraints and response gaps


    Via the South China Morning Post, a Reuters report: Chinese firm pushes Ebola drug it says can cure deadly virus.

    The report ends by saying

    “We have a myriad of connections with the military medical science units and have developed lots of products in cooperation with the AMMS,” Che said. AMMS is a research unit of the People’s Liberation Army.
    Che pointed out that a Chinese vaccine against a Sars outbreak a decade ago, also developed by the military, was approved by the drug regulator rapidly after its application, signalling that JK-05 could receive similar treatment.
    “At that time the whole approval process, clinical components and the period after was cut right down,” he said.

    Via WHO, a situation assessment: Are the Ebola outbreaks in Nigeria and Senegal over? No yet is WHO conclusion.
    And the New York Times has a piece in which thery quote WHO

    The World Health Organization reported sobering new figures Tuesday about the Ebola outbreak ravaging West Africa, saying the mortality rate had risen to 70 percent and that the number of new cases could reach 10,000 per week by December.

  17. Bloke down the pub says:

    Read somewhere that one of earliest cases in this outbreak went to a wedding where she infected maybe a dozen other women. One ‘Typhoid Mary’ early in the spread of the disease within a country might have a major impact on the rate of infection. So far, most of the infections in western countries have been amongst medical workers who would be conscious of the risks and aware of symptoms. Once out in the general population, those infected become far more likely to carry on with their normal routine and thus spread the disease in the population.

  18. Speed says:

    j ferguson:

    You’re right about the unrecognized value of personal history. My mother was working as a nurse the day of the Cleveland East Ohio Gas Explosion — something I wouldn’t know about except for her stories.

  19. Speed says:

    More on the Spanish Flu Epidemic …

    “Demonstration at the Red Cross Emergency Ambulance Station in Washington, D.C., during the influenza pandemic of 1918.”

    We’ve come a long way, babies.

  20. E.M.Smith says:


    See it? I posted about it ;-)

    Also looks like Selenium helps stop several viruses along with reduction in colon cancer risk and inflammatory diseases. ( I’ve started some. Does seem to have the joint discomfort backing off and my energy is up. Also Mg Citrate also reduces colon cancer lesions (at least in mice). Yes, two more papers I’ve copied intending a posting…. that now with the new computer I can likely make that happen. But for now, it’s enough just to say that Selenium seems important, and anti-HIV drugs may work.


    As long as we continue to have a ‘double’ every 3 weeks or so, we are losing. At “one for one” you have continued infection for years. It has to get to “less than one” new case per old case before things start to ramp down.

    Since we just got the 2nd nurse diagnosed with Ebola from just the first patient (and still have 14 or so incubation days to go for more to surface) we are already over “2 for 1” and thus still on the doubling time curve.

    This will get a lot worse before it gets better.

    Hopefully they will start enforcing more strict quarantine behaviour, restrict travel (for 30 days post exposure) for caregivers working on Ebola patients, drop a Field Hospital with CBW gear into W. Africa for any healthcare workers there who get exposed (i.e. stop flying folks out of whatever country they are in when they get it), beef up the protective gear (including bleach water washes prior to removing it…) and maybe, just maybe, find a working cocktail of drugs and vitamins and fluid support that extend survival.


    Thanks for the links!

    That Chinese drug is good news. Likely ‘yet another viral replication inhibitor’; but the more of them the better. As the disease mutates to resist one, the others can still work. They ought to be trialing that right now in some random village in Africa that otherwise has no hope at all…

    @Bloke Down The Pub:

    And thus the value of travel restrictions and quarantines. They need to set up borders, and places where folks get a free stay and food for 3 weeks+ before they can move on… and a field hospital for those who don’t get to move on…

    There is nothing at all wrong with a quarantine, or travel restrictions. It is simply recognizing that the disease needs to be contained. Same thing the body does when it walls off an infection to limit from becoming generalized “blood poisoning”. Prevents the “Average Idiot” from deciding they want to just treat it with smoking some M.J. and going to the party in the big city…

    Oh Well. The cat’s out of the bag now anyway. With 2 staff down, and who knows how many hundreds exposed ( IN the airplane, in the airport, in the taxi to the airport, in the bathroom at the airport, handling baggage, doing the TSA up close pat down, etc. etc. etc.) I would be stunned if there is not an added case or three in the next 4 weeks.

    We can hope… but… “Hope is not a strategy. E.M.Smith”

  21. tom0mason says:

    A possible infector in Turkey.

    A man arriving from Ivory Coast infected with the Ebola virus has been hospitalized in Istanbul on Wednesday.
    The patient was brought to the Marmara University Education and Research Hospital. He was diagnosed with Ebola after landing in Istanbul’s Sabiha Gökçen Airport. The hospital was briefly quarantined and current patients immediately were transferred to other hospitals.

    It’s a dramatic development, if true. But I can’t find confirmation yet in the Turkish online media.
    If it’s a real case, the Turkish authorities and media will let us know very soon. If it’s not, well, you can catch Ebola jitters even next door to ISIS with war in Syria and Iraq.
    And a source of information at
    where there is this graphic –

  22. Pingback: The Exponential of Ebola Rolls On | Musings from the Chiefio

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