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.