Ebola Math

"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...

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 [may] eventually die.

That process [according to present math] would be complete – worldwide – about June of next year.

The population [would] drop in half [if the math becomes a reality].

...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 [most likely purposefully low reported] total so far).

...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.

...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?

...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.

[One] 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...

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.

...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."


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