Holy fucking shit, you were seriously claiming to have performed a "thorough mathematical consideration" without looking at any data at all? In any case though you should look at all the other European countries with higher vaccination rates where measles is endemic too (such as the UK and France).
I stated quite clearly in the OP that the OP was about the case study of measles in America in 2014. Researching countries with lower rates of vaccination is not really relevant for the main question of "should our American 2014 policy be to push people to vaccinate higher than the current 90%?"
Since then, the thread has progressed to broader worldwide and more generic discussion.
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Regarding endemic disease and herd immunity thresholds, there are several considerations to take into account:
1) First of all, we have to consider that it is not actually necessarily needed to wipe out endemic disease in someplace like the UK YET, while we are still waiting on places like India with much higher population density, worse sanitation, and worse healthcare still being at 70%ish (IIRC) coverage. Even if there is endemic UK disease, if it's only among a few hundred people, most of whom are documented, then they present little threat to significantly spreading the disease elsewhere.
You have to consider the possible strategy of "Wait until all major countries that have air travel and contagion between them are within reach of possibly achieving wipeout levels of vaccination, and then simultaneously push up to those levels when everybody is ready" to actually achieve the wipeout.
Until then, you case the possibility that you are over-vaccinating (in terms of overall deaths from vaccines vs. disease) and killing unnecessarily many people while you are sitting around waiting for other countries, in the name of eradication which you already know isn't possible yet until those other countries catch up.
2) Ignoring #1 for now, the herd immunity thresholds published by the CDC and WHO are also NOT the levels at which endemic disease is containable. They are the levels at which outbreaks are not supposed to occur anymore. These are different things, for multiple reasons:
a) The reproduction ratio assumes a completely uninfected population (which stops being true after just the second infection and becomes progressively inaccurate)
b) The ratio assumes zero natural immunity (same story)
c) The ratio assumes natural spread with no government intervention (yet in reality we do have government intervention of course)
d) The ratio also often assumes pretty dumb behavior with regard to staying home when sick, etc. although this varies depending on who is simulating the ratio and what parameters they choose.
In reality, all of these and other factors can and do push the actual reproduction ratio way down below theoretical starting levels as an outbreak grows.
Thus, outbreaks can and do reliably fizzle out even with basic reproduction ratios well above 1.0Not infinitely above 1.0. At some point, it will overwhelm these factors and become endemic. But that point is not the same point as that suggested by herd immunity thresholds. It is X% lower, which experts might know, but since they don't publish those numbers, we can only make educated guesses in the thread. X is definitely > 0 though.
I am also confused about why you're arguing with me about "completely misunderstanding the concept" and yet later in the same post mention that the studies you cited discuss exactly what I'm saying above (that eradication can occur / endemic be avoided above ratios of 1.0). If you're hinging this entirely on this "critical community size" concept, you need to really expand on that a lot more, because from my understanding, the entire U.S. is not a "community" in that sense.