Seems like Europe, USA and other "first world" nations are getting the vaccine supplied and produced in this December.
In Europe it will (/should) take longer, because authorization takes longer. (Few more months.)
You are basically at the point, where an independent body has to look at the studies the manufacturer produced, and (where necessary) produce its own additional studies, to find out if it is "safe" for the vaccine to be greenlit for distribution.
US and Europe have very different models there. US basically has more of a 'you go try, and if you fail - you get sued out of existence' model. While in Europe its harder to get it cleared for public consumption, but then you face less legal risk on the backend. (You are generally not getting sued out of existence..
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Thats an overgeneralization, that sometimes even is different with different categories of drugs, but generally should hold true.
The issue with "generally should hold true" is, that none of the current situation is 'generally'.
You basically have politicians pressuring the 'independant bodies' to greenlight it faster, because they are under public pressure "to do something". Also - generally speaking...
(On the left the 'talking point' you hear on Colbert f.e. is "I would take it in an instance, if the FDA approves it, but not if Trump tells me to get it". Pretty useless talking point, but you get the notion..
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There are also PR/marketing plays in action where some people are pushing for medical personal to "get it first".
While medical personal is in the high risk group, and definitely WILL get it early - the other high risk group is elderly people. If you give it to medical personal first, average age would be lower, which means that cases of 'severe sideeffects' also would be lower, which means better press for the first months or so..
(Those are small considerations, but ones I cant help but noticing..
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In general, old people, medical personal and frequent travelers are first in line to get it. And rollout will take 2+ years, until you reach "heard immunity equivalent" numbers.
Also 95% or 90% effectiveness is almost exclusively PR. Thats not a number you should have to know or care about. If its lower you have to give people a second dose, a few months later. For the individual thats mostly irrelevant.