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I saw an interesting graph of % vaccinated over time in various countries.  Note this is percent of population, not percent of those eligible for the shot.   For the US, the CDC reports 41.3% of the population has at least one shot.  19.7% of the US population is under 16 and not eligible.  So, 39% of the US population has not yet gotten a shot but could get it.

In California, just 8 days into the opening of vaccines to the general 16-49 population, I expect there will be a large number getting their first vaccination over the next few weeks.

If you look at the above graph, the slope of the US vaccination rates has not started to level out.
Israel is the highest, at 62%, but it started leveling out at 54%.  Only 1.5% of their population has gotten a first shot in the past 3 weeks.

The UK is 2nd at 49%.  It started leveling out 3 weeks ago, and has increased only 2.6% during that time.

10.5% of the US has gotten a first shot in the past 3 weeks.
The CDC's graph of vaccination by age group shows about 81% of those 65+ have gotten at least one shot.  (7% in the last 3 weeks; 2% in the last week.)
The 50-64yo is about 60% vaccinated, but looks like it will level out below 70%.
The younger age groups are climbing fast but it is too soon to tell how high they will go.

Regionally, there are differences in % of eligible people getting at least one dose.  The lowest is just under 40% while the highest is about 72%.  The 72% seems to suggest that (smallish) state got more doses per capita than other states.  There are a number of states in the 60-63% range.

At least one news article I saw today suggested that vaccination centers in some parts of the US were closing from lack of demand.  I think people are now going to local pharmacies rather than vaccination clinics.
If I have my facts straight, The United Kingdom opted to do the untested and controversial approach of giving the second dose at 12 Weeks. Is it possible that the leveling of the curve is the result of constant supply but diversion to second doses. Note that it started leveling in the beginning of April, 12 weeks after they started.

I would normally assume that the UK would have an ever increasing supply, like the US. However, I just don't know.

The same comments for Israel, which started a month earlier.
Good point. But, that still leaves roughly 20% of Israel's adult population and 30% of UK's adult population without shots.

An optician yesterday indicated his son is in Canada, and that their 2nd shot was 4 months after the first, so they seem to be following the same model.