Bob Goodwin: A Layman’s Guide to the Mathematics of Ebola

By Bob Goodwin, an investor and medical device entrepreneur who lives in Mercer Island, Washington

Ebola is a very nasty disease, but it is actually fairly easy to understand mathematically, which is why the disease prevention folks are confident in the best ways to manage this epidemic that otherwise seems to be growing exponentially.

I was motivated to research and write this because my crude understanding of the disease was that it was doubling every 3 weeks and killing 70% of those infected. It was seeming to drive societies to a militarized quarantine that was doomed to create panic and fail, and the pandemic had long since overwhelmed the health care system in the region.
It seemed obvious to me that the pandemic could not be contained within any set of borders, and that there was a point that even our own, more extensive health care system would become overloaded, and our country would soon look like Liberia. However, this is not going to happen, and it can be explained fairly easily.

To research the math I downloaded an Excel spreadsheet from the CDC that modeled Ebola infections (here). It took me a few hours to pull out the key issues at play with the model. The most elemental mathematical issue is the transmissibility of the virus. 68% of transmissions occur in the first week of an infection, 26% in the second week, and 5% in the third week. Whether or not you survive, you will not get re-infected (or that is the theory). Of course dead bodies are infectious, but there is a belief that people learn pretty quickly how to avoid infection from a dead body.

According to the literature, every infection naturally causes an additional two, but as people learn, the rate of infection declines. Using the published rate of the existing pandemic progression, I calculate that the infection rate is currently 1.66, which is to say that even in Liberia they are learning pretty quickly.

If the rate (called R0 in the literature) remains at 1.66, the number of new infections will double every 3 weeks. There is a belief that only 20% of the population is naturally immune to Ebola, and with an exponential pandemic, 70% of the remaining 80% of the population will eventually die. That process would be complete – worldwide – about June of next year. The population will drop in half. Of course things like this have happened in history. But our advantage today is not medicine (Doctors don’t have much in the way of a cure for those that are infected). Our advantage today is information. We learn faster because information is accurate and flows better.

The mathematically critical point for the virus is when R0 crosses below 1. At this point the infection rate stops growing, and starts fading. If we can get R0 down to .3, the pandemic will end in 3 months, although the death toll may still double in that period. Even if we could get the number down to .8 immediately, we would limit the death toll to 24,000 (6 times the total so far).

I would note, as a starting point, that the sole fatality in the United States was released from the hospital for 3 days with a fever of 103. He was susceptible for 3 of the roughest days of infection, and he likely should have infected at least one other person, but he did not. The story of the family was one of supreme vigilance. His family was so sure he had Ebola, that they took great care not to be exposed, and they succeeded.

The model used in the CDC spreadsheet involves a calculation of what percent of patients who are infectious have been properly isolated. If R0 is naturally 2.0, then it is sufficient to isolate more than 50% of infectious people. We need to assume that some people will hide, or be scared and careless. We also need to assume that some people will be unaware that they are infectious because waiting until you are symptomatic is somewhat late in the process, which is why the CDC will try to track down potentially exposed people and quarantine them prior to the onset of symptoms.

It is obvious to me that controlling R0 requires a modestly functioning society, and is even better if the pandemic is small enough to still be manageable by our CDC or military. But beyond some breaking point for the society, R0 will rise again. But what chance is there, that we will lose control of the pandemic in western societies?

It seems abundantly clear to me, that even without hospital beds, we can isolate far more than half of the outstanding cases of Ebola in any western country, so that small numbers of infections will likely never grow exponentially.

The possible hole in the logic is the assumptions that only small number of infections will arrive here. There are only so many airplanes that arrive each day, so that in itself is not a threat to overwhelming our infrastructure. The only potential risk is panic migration across a border. So if Mexico were to lose control of the Ebola battle through extreme mismanagement, it could break our natural defenses. But this seems unlikely.
However there are no such limitations in Africa, and it is entirely possible that panic in Africa could keep R0 above the critical level, and the virus could cut the population of the continent in half. This of course, is why it is such a good idea to get boots on the ground in Africa. Managing R0 is all about information and isolation. Force can lead to panic, and cultural difference could make it hard to inform. However we all have a natural survival instinct, and my bet is that boots are a great way to reduce R0, whether they are US military, volunteers, nurses or doctors. There just have to be a sufficient ratio of boots to infected people.

We are fumbling 3000 Army personnel (That would be 6000 boots) into a region with 15,000 infections. In three weeks there will have been 30,000 infections. The longer we wait the harder it gets.

So the estimate of how bad it can get depends heavily on how quickly R0 can be lowered. The worst case estimate is probably in the range of half the population of Africa. But the working worst case estimate is about a million. In the latter estimate, the presumption is that the population figures out by itself how to quarantine the sick, and the pandemic burns itself out, without much help from the west.

But I still think it is a good idea to get boots in there quickly.

Print Friendly, PDF & Email


  1. Vatch

    “I would note, as a starting point, that the sole fatality in the United States was released from the hospital for 3 days with a fever of 103. He was susceptible for 3 of the roughest days of infection, and he likely should have infected at least one other person, but he did not. The story of the family was one of supreme vigilance. His family was so sure he had Ebola, that they took great care not to be exposed, and they succeeded.”

    We now have learned that a nurse who treated him has the disease. As for his family, they’re not out of the woods yet, since the ebola incubation period varies, and can be up to 21 days. The patient who died arrived in Dallas on Sept. 20, and showed symptoms on Sept. 24. If we count from Sept. 20, the family is safe; if we count from Sept. 24, they still have a day or two before they’re safe. But they were exposed for a few days after he was first discharged from the hospital. So we really need to count from Sept. 28, when he was vomiting and he was sent to the hospital the second time. His family still has almost a week before they can be considered safe.

    1. sgt_doom

      Except!!!!! You are neglecting to mention the important variable that Ebola virus can exist for up to 23 days outside the human host in liquid or on dried material — or both!
      Why this is not frequently mentioned by all these so-called experts baffles me!

      1. Vatch

        Thanks. I found this (most recently modified Aug. 22, 2014 – selected text emboldened by me):

        SURVIVAL OUTSIDE HOST: Filoviruses [such as ebola] have been reported capable to survive for weeks in blood and can also survive on contaminated surfaces, particularly at low temperatures (4°C) One study could not recover any Ebolavirus from experimentally contaminated surfaces (plastic, metal or glass) at room temperature. In another study, Ebolavirus dried onto glass, polymeric silicone rubber, or painted aluminum alloy is able to survive in the dark for several hours under ambient conditions (between 20 and 250C and 30–40% relative humidity) (amount of virus reduced to 37% after 15.4 hours), but is less stable than some other viral hemorrhagic fevers (Lassa). When dried in tissue culture media onto glass and stored at 4 °C, Zaire ebolavirus survived for over 50 days. This information is based on experimental findings only and not based on observations in nature. This information is intended to be used to support local risk assessments in a laboratory setting.

        A study on transmission of ebolavirus from fomites in an isolation ward concludes that the risk of transmission is low when recommended infection control guidelines for viral hemorrhagic fevers are followed. Infection control protocols included decontamination of floors with 0.5% bleach daily and decontamination of visibly contaminated surfaces with 0.05% bleach as necessary.

      2. bob goodwin

        The potential flaw in any analysis is the unknowns, and in Ebola there are many. The potential flaw in all rebuttals of the unknowns is the assumption that people don’t learn. It is true that the models place zero weight on transmissibility of viruses outside of live bodies, and it is also true that such weight is clearly greater than zero, I share the belief with the models that these external viruses have negligible impact on the transmissibility factor. The primary reason is that it is a lot easier to isolate non living things. The secondary reason is that the coefficients of transmissibility on non living things is much lower. If you want to reduce R0, you focus on the big ticket items. The goal is get R0 below 1.0, not to boil the ocean.

  2. Diego M

    I’d like to ask about the main problem I see with your analysis. To what extent are African data reliable? The New York Times has reported that graveyards are having many more Ebola-suspected deaths coming in than officially recognized, so that figures may be wrong even by orders of magnitude (meaning e.g. 20,000 dead instead of 4,000). Since figures are unreliable, to what extent can an analysis based on those figures be reliable? I am just asking, since I have no knowledge on this topic.

    1. Yves Smith Post author

      This is a disease transmission model based on the normal evolution of infectious diseases. Ebola initially had a 90% mortality rate, which actually meant it was not a candidate for a pandemic. It killed its victims too often to infect many people.

      By contrast, the last pandemic, the Spanish flu of 1918-1919, had a 2.5% mortality rate but was highly infectious. So the vector to watch is how infectious it becomes.

      1. Slick

        This is truly the issue. I am all in the “do not panic” camp, but realistically every human vessel with the infection is trillions of replications and viruses are notoriously sloppy in their reproduction. The mutation to “airborne” may never occur, but what about a mutation that allowed the victim to live another week or two with the virus? Not impossible. This could be a major problem regarding R0 1:1.66.

        I am encouraged but the author’s math, and I think he is persuasive, but there are many dark and frightening things about Ebola, and they math only accounts for the part we know about. It is important to recognize that it gets harder to stop everyday (as long as infections are growing) and geographical boundaries like borders and oceans are not an impediment that will stop the virus.

        My neighbor is an infectious disease doctor. She’s seriously considering going to Africa in the next few weeks to help. She is young, has a great job, wonderful life and home, and a three year old daughter. If you think it isn’t serious, ask yourself why she is considering going.

        1. MyLessThanPrimeBeef

          I wonder if the rate of mutation can speed up when

          1. the virus shows up in a new continent, a new enviroment
          2. the host population size increases (bigger virus population, reproducing more often)
          3. encounters more experimental drugs

          1. MyLessThanPrimeBeef

            I think I found my answers below by Bart Fargo and my questions are better framed with ‘the number of mutation events’ instead of ‘rate of mutation.’

      2. bob goodwin

        I am not sure that your statement is true Yves, I think transmissibility and mortality are not as tightly coupled as you imply. Clearly if you live longer there is more time to transmit the disease, but Ebola transmissibility drops quickly, and people die slower than the transmissibility drops. The Spanish flu had the challenge that is was difficult to isolate, but I think it actually did not have that high an R0.

        1. Yves Smith Post author

          As I understand it, the more people who get a disease and don’t die of it, the better the odds it has of mutating, which includes mutating to more transmissible forms. That’s the link between the increase in transmissibility v. the decline in mortality.

          The Spanish flu “had a profound virulence”:

          1. Bart Fargo

            A virus mutates at the same rate whether its host lives or dies. Even a highly pathogenic virus like ebola can mutate throughout the course of an epidemic, and the number of mutations (beneficial or non) increases with the number of replication events, which is directly related to the number of patients infected with the disease. So although ebola has about 1/4th the mutation rate of influenza A, the total number of mutation events depends on the level of virus replication in the host as well as the number of hosts infected. This is why it is important to get the epidemic under control quickly, as not only will more people die but it is realistic to expect that chance mutations that increase transmissibility will be selected for the longer the epidemic continues. After the epidemic is stamped out, the ebola virus will still persist in animal reservoirs, but the selection pressures will be different than among humans. Transmissibility itself depends less on mutation rate and more on factors like whether or not the disease can be spread by the airborne route (like the Spanish flu, but not ebola), and how contagious the infected become, and for how long, before they can be detected and isolated (the flu can be spread before the appearance of symptoms).

            1. lee

              One of the several experts (I’ve forgotten which) often appearing on radio and tv has stated that no human virus has ever mutated to change its mode of transmission.

              This from a Q&A at the New York Times<a reiterates:
              "No one can say exactly what the likelihood is that the virus will mutate to definitively become airborne, but it is not thought likely. No virus has ever been known to change its mode of transmission. H.I.V. mutates incredibly rapidly — as much in one day as flu does in a year, according to C.D.C. scientists, and H.I.V. has not become airborne."


              1. Bart Fargo

                Yes, a complete change in the mode of transmission is unlikely. But possible mutations could include growing to higher titers in patients’ excreted fluids, milder onset of symptoms, or greater ability to cross mucus membranes. Small changes can still make a difference in a large epidemic.

    2. bob goodwin


      I created my own model and changed a broad range of assumptions, including the specific questions you asked. The answer is the only number that really mattered was R0. If I assume the starting point is ten times higher, then the output is ten times higher. If I assume that R0 cannot be lowered below 1.0, then humanity is lost. But all we have to do to lower R0, is to cut the transmission rate in half, which may not happen until we learn our way through the first few hot spots, but will occur in west quickly, and in the 3rd world eventually.

      1. Diego M

        Thanks a lot, Bob. What I was rather referring to is the fact that maybe R0 is not calculated on a reliable basis, since death tolls are not that reliable. Our own First-World experiences with Ebola, both in Spain and in the United States, point to a lot of unknowns. How did the nurses get infected? No one really knows. People keep on saying that HIV is less contagious than Ebola, but nurses don’t need space suits to treat people infected with HIV. Basically, you don’t expect a nurse to contract HIV unless they get a needle stick or another noticeable accident. This hasn’t happened neither in Spain nor in the US. Morever, the African R0 cannot be extrapolated to First World countries. If you beat with my overdone comparison, being in the middle of the jungle with very few humans around is not the same as taking the underground (coughing and sneezing), vomitting in an emergency room full with people or getting First-World care, which poses risks unheard of in Africa (intubation, dyalisis, etc. are procedures which don’t exist there). Basically, what I mean is that you don’t expect First-World countries to completely isolate groups of people and let them die virtually unattended, even if that would help stem the epidemic. In fact, you don’t expect e.g. the US to do that even if the potential source of infection is just a dog. Ethics apart, this should be reflected in a different R0.

      2. Diego M

        Thanks a lot, Bob. What I was rather referring to is the fact that maybe R0 is not calculated on a reliable basis, since death tolls are not that reliable. Our own First-World experiences with Ebola, both in Spain and in the United States, point to a lot of unknowns. How did the nurses get infected? No one really knows.

        People keep on saying that HIV is less contagious than Ebola, but nurses don’t need space suits to treat people infected with HIV. Basically, you don’t expect a nurse to contract HIV unless they get a needle stick or another noticeable accident. This hasn’t happened neither in Spain nor in the US.

        Morever, the African R0 cannot be extrapolated to First World countries. If you bear with my overdone comparison, being in the middle of the jungle with very few humans around is not the same as taking the underground (coughing and sneezing), vomitting in an emergency room full with people or getting First-World care, which poses risks unheard of in Africa (intubation, dyalisis, etc. are procedures which don’t exist there). Basically, what I mean is that you don’t expect First-World countries to completely isolate groups of people and let them die virtually unattended, even if that would help stem the epidemic. In fact, you don’t expect e.g. the US to do that even if the potential source of infection is just a dog. Ethics apart, this should be reflected in a different R0.

        1. Sam Kane

          Also the so called “first world” (if that can be said of a rich place where a poor patient with 10 degree fever gets sent home to save money) has lots of cold weather to help preserve the virus and increase transmission possibilities.

  3. abynormal

    There just have to be a sufficient ratio of boots to infected people.
    have i missed infected boots in the equation ?

    1. bob goodwin

      Boots lower R0 to the extent they assist in information and isolation. They raise R0 to the extent that they increase R0 by becoming infected. But the key is that humans learn, and always have in every pandemic even in medieval and ancient times. A linear investment in boots should have an exponential payback in lives.

      1. pat b


        I was playing with the numbers and there appears to be some sensitivity to the size of the initial infected pool. Given the number of days gone by and the relatively large pool of the infected, i started the infection not at 25, but at 12000 and played with longer periods of infection…

        It doesn’t look good.

        I think in the G-20 we can keep control, but, i wouldn’t want to be in africa.

  4. jgordon

    “disease prevention folks are confident…”, “…CDC”

    That is clear evidence that it may be a good time to consider panicking.

    ‘When it becomes serious, you have to lie’ – Jean-Claude Juncker

    If only we had people in authority who were not known liars. Then maybe we could trust some of the things they are saying. Ah well.

    1. bob goodwin

      I am in your camp that the greatest cost of corporatism may be the lost of trust in public institutions. That is why people (like me writing this article) need to be committed to truth, regardless of whose ‘team’ the truth helps.

      Panic is a great tool for politics. We need to have boots to manage the panic too, a linear investment can have an exponential payback.

      1. pat b

        i worry about two kinds of panic from Ebola.

        1) A mass panic of people going everywhere. The manic squirrely thing. that would cause the disease to spread like wildfire.

        2) A mass panic and shutdown of global trade. That would really kill people.

  5. marcum

    Any media analysis of what happens if / when this hits the huge densely populated cities in developing countries outside Africa? Sure the US Canada and western Europe have robust health systems. But what about the slums of Mexico City, Karachi or Sao Paulo?

    1. Foy

      Yes, I think that is the next issue, if/when Ebola reaches places with densely populated areas in Central America or India or even Chinese provinces (there are many Chinese workers in Africa). Central America is obviously on the US’s doorstep with significant population movement across borders.

      US Marine Corps General John F Kelly talked about it at a recent conference:
      “By the end of the year, there’s supposed to be 1.4 million people infected with Ebola and 62 percent of them dying, according to the [Centers for Disease Control and Prevention]. That’s horrific. And there is no way we can keep Ebola [contained] in West Africa.”

      “If the disease gets to countries like Guatemala, Honduras or El Salvador, it will cause a panic and people will flee the region, the general said. If it breaks out, it’s literally, ‘Katie bar the door,’ and there will be mass migration into the United States,” Kelly said. “They will run away from Ebola, or if they suspect they are infected, they will try to get to the United States for treatment.”

  6. Brooklin Bridge

    If anyone or anything can make things worse, our for profit health care system can be counted on to do so. They can only be outdone in this endeavor by our politicians who have a stunning track record in putting the average citizen in harms way or making absolutely sure not to intervene if their corporate masters do so first.

    If Ebola has any intrinsic restraints – and it apparently does – and/or if there is any other good news coming from nature or other areas not related to our rotten helath care system or our beyond rotten politicians, you can be sure that those rapacious health care insurance companies will take credit for it along with those corrupt politicians.

    Petter’s link has a very good summary of the risks involved and a gloomy but probably accurate description of where things are going. Little will be done to eliminate Ebola (not enough profit) and it will remain worst for 3rd world countries and in in developed countries the poor and not so wealthy will be most affected. Like HIV, it will be contained; the wealthy having the greatest protection. But it is very unlikely it will morph into a major plague like disease. Most likely, Texas will continue to kill off more of it’s adults and children by lethal injection than by negligence with Ebola – though it may be close.

    1. bob goodwin

      My argument is that Ebola is a not controlled by the health care system. They have very little to offer, except fluids, for the infected. The key is containment, which is certain to get political support from all corners.

  7. VietnamVet

    I agree with the math. My only question is if there is the political will to spend the money needed to reduce the R0 to less than one before the medical system and economy collapses locally in a hot spot. We are waiting today to see if the Ebola virus is propagating successfully in Dallas and Spain or not. If one more person is infected at each place, the initial R0 there will be 1.0. If the virus is establishes itself in a population a crash program has to be started to build holding centers for those exposed to infected persons and expand the testing facilities so that everyone exposed can be tested for the virus.

    The West doesn’t need any more hot spots. Everyone leaving West Africa must be quarantined for a minimum of 21 days and tested to be free of the virus before being released into the population.

    I find it very strange that public health policy is being decided based on economic beliefs of free trade and travel rather than mathematics and science. The West did not help to quarantine the initial Ebola outbreak in Africa and let it burn itself out as it has done before. The Ebola virus appears to be established permanently in West Africa. The only question is how many people it kills as it spreads worldwide.

    1. Sam Kane

      veryone leaving West Africa must be quarantined for a minimum of 21 days and tested to be free of the virus before being released into the population. I find it very strange that public health policy is being decided based on economic beliefs of free trade and travel rather than mathematics and science.

      Odd that you note that those in charge of public policy are driven by #economic beliefs” as you put it, but then you overlook the possibility that in fact the might actually be implementing “health” policies consistent with those belifes.

      Look: it is fairly clear by now that the small handful of people on the planet who own the assets, control the govts and dictate public policy: are busy accumulating every grubby little penny they can and now see human capital as surplus to their requirements. Everything we read even here on this blog, points in that direction.

      So regarding lack of Ebola containment policies. Draw your own conclusions – I certainly have. There is very good math and science behind that decision, let’s put it that way……

  8. bob goodwin

    Our politics gives us our first impulses, but every person will abandon political beliefs for survival. I would cite your example of 21 day quarantine for all migrants as an example of a first impulse on your part that is probably shared by others. This approach would be valid if we needed to get R0 to zero. But it is a massive misuse of resources if the goal is get/keep R0 below 1.0..

    1. James

      Hey Bob. Perhaps you could discuss the logistical details and concerns of a large scale quarantine effort. Wouldn’t this be quite an undertaking if required on a large enough scale (say several thousands or tens of thousands)? For instance, wouldn’t those being quarantined have to be segregated chronologically, perhaps down to the day (meaning at least 21 groups, so as to keep a single positive in any one group from polluting the whole larger group), at which time if someone demonstrated positive, everyone in that group would have to be recycled back to day 1 and/or segregated as a separate group themselves, and so forth? Perhaps I’m over thinking this, and I’m certainly no expert in any of this, but the logistics (and the tempers, and the opportunity for errors) would seem at first blush to be quite daunting. Has anyone thought all this through yet?

  9. Oregoncharles

    The family didn’t become infected, but a nurse in full gear did? In Spain, too? What about the emergency room personnel that treated him and sent him home? None of them were infected? (They’re probably in quarantine now – but what about all their contacts?)
    There’s something wrong with the picture. It looks like infection doesn’t happen quite the way they say it does.

    1. bob goodwin

      You are correct that we have a lot to learn about the transmissibility of Ebola. But that does not undermine the fact that humans learn quickly, and only need to keep R0 below 1.0.

    2. financial matters

      This seems more likely to infect health care workers esp through vomit and diarrhea unless the home contacts are also close care givers. This series of short on the ground videos mentioned by redleg are very good. The reporter wisely decided not to go into the treatment room. One reason was the difficulty in safely taking off protective gear.

      Very interesting reporting here:
      3 parts.

    3. Bart Fargo

      Not really. It is somewhat surprising that no one in the family was infected despite living with a symptomatic ebola patient for 3+ days, but it sounds like they took precautions not handle any of his infected fluids. The nurse, on the other hand, was in intimate and daily contact with his infectious fluids (and ebola is a very messy disease). The precautions the hospital used are enough to protect workers, but only as long as no one makes so much as a small mistake in protocol. That is why higher precautions (respirator instead of a mask+shield, isolation suit instead of gown+apron), although theoretically unnecessary, will better protect workers because in the real world even well-trained people sometimes make mistakes, and higher precautions provide better protection against such mistakes.

  10. Lyle

    I would not that the processes for disposal of corpses in the US are very different than those in West Africa, resembling the practices used in the US 150-200 years ago. Corpse disposal has been moved from the family to professionals for the last 100 years in a majority of cases. Further based upon what happened with the US fatality, it appears that rapid cremation becomes the only option for a person dying from Ebola in the US. Basically you bag the body and take it right to the crematorium.
    Now the obvious question is what would it take to introduce cremation into Africa.

    1. Bart Fargo

      Cremation is currently being practiced in Liberia for bodies of those who died of ebola. Team of trained hazmat workers, working with the government and the Red Cross, visit hospitals and homes to properly retrieve and cremate bodies. The capacity of these teams, however, is overwhelmed the sheer number of deaths, just as the capacity of the country’s health system is far, far overwhelmed by the size of this epidemic, even when factoring in current levels of international aid. More treatment and isolation space is desperately needed, and I hope more capacity is what US troops will be able to deliver.

    2. vlade

      I’m told that Liberia now requires cremation for Ebola victims, but often it means that the families don’t report the death or try to bribe the body collectors so that their dead can get traditionall burial (which, again I’m told, includes kissing the departed to say farewell… ). Third hand information, caveat emptor.

  11. Lune

    I agree with your overall emphasis on established public health principles, like R0 and transmission rates. However, I do think that the numbers you use may be inaccurate, and they don’t need to be inaccurate by much to lead to much more catastrophic results.

    Firstly, the R0 of the current ebola spread is estimated at 2. Like other commenters have argued, this is based on a severe undercounting of dead and infected patients. With a lack of public health monitoring, the transmission and death rates, I suspect, are far higher than we currently know.

    Changing the R0 from 2 to 3 or higher makes the task of bringing it below 1 much harder. Indeed, I would argue that even reducing it from 2 to 1 (i.e. reducing transmission by 50%) is much harder than it sounds. Given that even after sounding the alarm bells and overreacting to the presence of Eric Duncan (hazmat suits, negative pressure isolation, etc.), he managed to infect 1 other person. IOW, even with a gross overreaction and an abundance of precaution, our small sample size of n=1 has an R0 of 1.

    While you’re correct that people learn more as the epidemic progresses, it’s also true that resources are strained as the epidemic progresses. At some point, all the learning in the world will not help if we overwhelm our ICU bed capacity (~60,000 adult ICU beds in the U.S.), or strain other medical resources (nurses, etc) at which rate our death rate (and most likely our transmission rate as well) will climb.

    An instructive example is to look at healthcare workers in the epidemic areas. While they may suffer from lack of resources, they are certainly not dumb, and are well experienced (by now, but even before) in dealing with Ebola. And yet, they have a higher fatality rate and their transmission rates (albeit not from worker-to-worker transmission but from patient-to-worker transmission) do not appear to be falling.

    Similarly, isolation is very hard. Looking at historical quarantines (e.g. for the Black Death, the flu, etc.), it is sobering at how brutal and unjust the measures can be (in the Black Death, some quarantines were enforced on pain of death). Indeed, even modern quarantine laws are amazing for the types of powers that are deemed necessary to be effective. It is not clear that we as a society yet have the political or social will to implement such draconian measures. This will be especially true in the setting of mass panic and widespread suspicion of (if not outright rebellion against) public authority. Just look at Liberia for a sense of how hard it is to implement proper quarantine and isolation precautions. If 3,000 Army personnel are inadequate for Liberia, how many will be required for the U.S. and/or Europe? And will ordinary Army soldiers be willing to follow orders when it involves potentially condemning fellow countrymen to a near-certain death in a quarantine in order to save others?

    The techniques of containing an infectious disease have been known to people since before we knew what microbes were. But condensing that wisdom into a dry discussion of R0 and isolation protocols discounts the incredible practical challenges of implementing those techniques in the setting of mass panic, incomplete information, and plain human fallibility that severe epidemics usually entail. While I still believe this epidemic will be contained, I think it will be far harder than people think, and has a higher chance of breaching containment than the CDC currently thinks.

    1. bob goodwin

      You raised two excellent points, and I have thought a lot about both of them. While I dismiss a lot of factors as noise in the equation, R0 cannot be dismissed as a minor point. And I made some assumptions that I am not fully qualified to defend, but I think they are more sound than you say. The first assumption that I used was the R0 was capped at 2.0. I made this assumption from two sources of data. First, Ebola testing has been done on primates, and measured in with past outbreak field data. It is not a number that I would use to risk the world on, but I think it a consensus number of people who study this field. The second assumption is about the mutation of the disease making it more transmissible. I know there is a lot of discussion about this possibility, however the articles I read on this subject stated that transmissibility does not happen in small increments. Blood droplet transmissibility is similar over different viruses, and airborn viruses are far more transmissible. Ebola is not going to change from a bicycle to an airplane from a migration. So while it is not physically impossible to rule out, large increases in transmissibility are not expected.

      Your second excellent point of ‘dry R0 analysis’ is fair, but I concluded it was incredibly important. Of the dozen or so scenarios that we are discussing in American media, very few have any bearing on the outcome of the disease. A nurse catching the disease in Dallas is a disaster for her, her family, and even her hospital. It may even be a temporary disaster for Public relations, and health care overall. But what it is NOT is a disaster for the pandemic. We have an R0 right now of exactly 1.0, and we are learning quickly.

      The issues that you say R0 discounts (protocols, challenges, panic, poor information, fallibility) are important discussions. But I argue that have a simple metric (R0) that is the guiding metric for our society will do more for focusing our protocols, challenges, panic, poor information and fallability, as apposed to screaming about how horrible it was a nurse got infected. The disease is conquered with a simple metric called R0, now lets maximize our assets against that goal.

      I was motivated to write this because the information and fear were starting to infect our politics. We need to have a simple message: “Its R0, stupid”, and I saw nobody doing this.

      1. bob goodwin

        I will simplify the point even more.
        Big scary policy initiatives need simple story lines to keep society on board.
        “Ebola will be tackled in every country where we can get R0 below 1.0, and here are the best actions to accomplish that.” Then report R0 in every discussion of Ebola, so people can tell how we are doing.

        This is not minimizing the challenges, it is simplifying the message so it can succeed.

        Big CDC people and Obama should be explaing and tracking R0 publicly in every single press briefing, rather than trying to talk down every new tragedy.

      2. Lune

        Hi Bob,
        Thanks for replying! I agree that emphasizing R0 as an overriding goal allows us to focus our efforts. That said, I’m not so sure that emphasizing R0 will do much good when it comes to educating the public. But I suppose that’s the case with lots of complex public issues (what the public wants to hear vs. what they need to know :-)

        As for the actual R0 number, I do agree that 2 is our best estimate, based on the data we have now. People far more involved in this than myself have come to that conclusion and so I do believe it’s our best estimate at this time. But… these numbers can change as more data is accumulated. And I fear that the data will likely end up revising the R0 upward for several reasons.

        Firstly, like I said before, we don’t know the actual numbers of dead and infected people. Of course, public health officials understand this as well and have done their best to estimate the true numbers. But I think even those numbers will turn out to be under-estimates. Mainly because the number of uncounted infections keep getting revised upward (independently of the increasing number due to progression of the disease).

        Also, while I don’t think the virus will mutate in any significant way during the current epidemic, (especially not become airborne or something as people fear; although to laypeople the difference between droplet transmission and true airborne transmission is academic…), it likely did mutate slightly from the original ebola Zaire strain (probably becoming *less* deadly, or at least a longer incubation period), which allowed the current epidemic to not burn out rapidly in the rural regions where it first started, but rather smolder until it hit the cities. This is compounded by the fact that previous outbreaks were in rural regions where isolation and containment are much easier. We have very little data on transmission patterns in dense, urban environments which now comprise the main areas of infection. All that is a long way of saying that previous studies on primates, and even epidemiologic data on previous outbreaks may not be accurate for the current strain. Given that all the ways in which this epidemic is different, are ways that point to a higher R0, a reasonable assumption is that its R0 is higher than what historical data might suggest.

        Anyway, I’m not ready to head for the hills just yet :-) But I do think that all the uncertainties in our information are more likely to lead to revising numbers upward rather than downward, meaning, IMHO, the job of containment is likely to be harder than what most authorities believe.

    2. craazyboy

      From the CDC Respirator fact sheet:

      Just substitute Ebola wherever you see SARS and forget about the public misinformation that Ebola is not an airborne transmitted virus. Here they infer SARS IS airborne transmitted – the definition IS whether it can be transmitted by droplets from a sneeze or cough.

      Also, in one of the above reports, now someone is saying the virus can live outside the body for up to 21 days. So watch out for doorknobs too. And whatever get touched after a doorknob. The less scary sweat transmission mode could be at work here as well.

      “Understanding Respiratory Protection Against SARS

      SARS (severe acute respiratory syndrome) is a new respiratory illness that has been reported in Asia, North America, and Europe. SARS appears to spread primarily by close person-to-person contact with symptomatic individuals (e.g., persons with fever or respiratory symptoms). SARS can be spread by touching the skin of other people or objects contaminated with infectious droplets and then touching the eyes, nose, or mouth. Contamination occurs when someone with SARS coughs or sneezes droplets onto themselves, other people, or nearby surfaces. It also is possible that SARS can be spread further through the air by very small particles. This method is called airborne transmission, but investigations to date suggest that this type of transmission is unusual. It also is possible that SARS may be spread by other ways that are currently not known.”

      1. steve

        It can survive for a long time under ideal conditions, i.e. low temperature, high humidity and in the dark. Under real life conditions it does not survive long.


      2. vlade

        Ebola virus can survive (possibly), but AFAIK to enter the body it has a limited number of options – open wound, eyes… I’m not sure whether it’s transmisible via inhalation (transmission via inhalation is part of the “airborne” infection)

  12. Synoia

    You are assuming the numbers from West Africa are accurate. Precise they might be, accurate not at all.

    There are probably thousands, if not hundreds of thousands dieing out in the villages in the bush.

    “and the pandemic had long since overwhelmed the health care system in the region.”

    What health care system? There are no Government services, no public health services, nothing.

    1. bob goodwin

      As I stated earlier, the analysis does not sensitive to field data from Africa. To the extent that I measured R0 at 1.66 based on the doubling of deaths every three weeks is far from perfect. But the reset of my arguments hold equally well if R0 were currently at the top end: 2.0.

    2. Yves Smith Post author

      You are missing the point. The issue is not the total number of deaths, it is the transmission rate. You can have thousands of uncaptured deaths in the hinterlands without that affecting the transmission rate. Bob said the transmission rate was based on study of the disease in the wild. Ebola is not a new disease. It’s been around for at least two decades.

  13. Code Name D

    I will also add in a few new wrinkles. According to the CDC scenario, Ebola will not be an issue because communications are so much better in the US than in Africa. So information on how to control the spread will decimate quickly. To which I note, so too shall counter-information.

    That’s the tragedy that we are flirting with here. The CDC may be correct (and I tend to think they are) in that this is controllable and that we can burn this out quickly. But they have to be aggressive with the point-blank unvarnished information. Obama needs to be brutally frank here. It may cause some panic in the short term, but as people come to rap their minds around the situation, they will be able to adapt.

    That’s not what we are getting here. So far, it’s just Pollyanna Positivism that has already been proven wrong at least once. They said it could never get here – it not only got here but slipped right through the healthcare system with just a prescription for some antibiotics. Then we get “corrections after the fact” regarding the failures of the computer system to adequately notify. The people are NOT falling for that. The staff on the front line knew it was Ebola, or at least feared it to be, but couldn’t take charge of the system because of the corporate profit model. Obama is in delusions-of-adequacy mode, more concerned with deflecting criticism away from Obamacare than he is in taking charge.

    In the mean time, there is an information void and conspiracy theories are already popping up to fill it. Anti-vaccers are calling this a false flag operation to scare people into taking vaccines. The birthers think this is Obama’s attempt to remove Texas from the electoral map.

    Once the counter-information sets in, just simply disseminating information to the public is no longer sufficient. You also have to debunk the counter-information and then deal with the reality that a certain percentage simply can not be reached at all. They will flout the recommendations out of spite.

    1. EoinW

      Exactly right! Information makes us better suited to handle Ebola today, however our politicians and corporate media have a track record of manipulating information. We are only empowered if we know the truth. Can we trust the information coming from sources more interested in how they appear publicly and the economic impact?

      I had to laugh as Canada has finally started screening travellers from west Africa. Does this mean in six months time we’ll begin screening people coming from infected areas in the USA? Then again, Belleville, Ontario has a suspected Ebola case(just one hour drive east of where I live). Don’t anyone invite me for dinner any time soon!

      As with our economic problems, containing Ebola faces the obstacle of an elite which may, or may not, have the best interest of the general public in mind.

  14. Ernesto Lyon


    People In the Western World Need to Know What’s Happening Here in West Africa. THEY ARE LYING!!! ”Ebola” as a Virus Does NOT Exist and Is NOT ”Spread”. The Red Cross Has Brought a Disease to 4 Specific Countries for 4 Specific Reasons and It Is Only Contracted By Those Who Receive Treatments and Injections From the Red Cross. That is Why Liberians and Nigerians Have Begun Kicking the Red Cross Out of Their Countries and Reporting In the News the Truth. Now Bear With Me:


    Most People Jump to ”Depopulation” Which is No Doubt Always on the Mind of the West When It Comes to Africa. But I Assure You Africa Can NEVER Be Depopulated By Killing 160 People a Day When Thousands are Born Per Day. So the real Reasons Are Much More Tangible.

    Reason 1:
    This Vaccine Implemented Sickness Being ”Called” Ebola Was Introduced Into West Africa for the End Goal of Getting Troops on the Ground In Nigeria, Liberia, and Sierra Leone.

    It looks loopy on first glance, but there is plausibility. How many of these facts actually checkout? I know some African nations are trying to expel the Red Cross. It wouldn’t be the first time that medical aid gets mixed up with nefarious plots.

    The whole Ebola thing doesn’t add up.

  15. Thor's Hammer

    As others have pointed out, the state of data collection in affected areas is at best questionable and erratic, and thus a more accurate projection should include a probability curve of rather than a assumed number. But that issue aside, I think any real assessment of risk should include the question of viral mutability.

    If we change the initial assumption of transmission rates of 2.0 to reflect a strain that can be aerosol transmitted for a range of 10′ and remain viable for x time, does your thesis that the disease will naturally run its course still hold? (not unreasonable given that there is some evidence of aerosol transmission already)

    1. Yves Smith Post author

      Apparently viruses that infect via fluid transmission don’t morph into aerosol transmission. However, it may be that Ebola is unusually virulent for a virus that transmits via that route, as in contact with a very small amount is enough to produce an infection.

  16. vlade

    Thanks Bob. My thinking from the start was that to control Ebola (and similar) much more has to be done with restricting the spread rather than vaccines or miracle cures (AFAIK, there’s no good antiviral medicine in existence, regardless of the PR of Tamiflu and others..)

  17. Sam Adams

    The analogy is to the first infections of Justinian and the Byzantine empire in the 500s. Not the Spanish flu or hiv.

  18. IdahoSpud

    OK, so as of today, we have a second infection. The mathematics now is that the infection rate (under tightly controlled conditions, and with a high level of medical competence) is R0=2. Color me unimpressed with the CDC’s complacency.

  19. techeye

    I’ve never been to Africa. But the assumption that there is something special about our society that will prevent the spread of the disease here seems dubious at best. We have no shortage of poverty, ignorance, and superstition. CDC Director Frieden is no doubt a smart man. But his prediction that Ebola can be stopped relies on human beings thinking and acting rationally – sometimes not in their own best interest.

Comments are closed.