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But Sweden has had a lot more deaths compared to peer nations.

I find the most useful number to watch is 7 day rolling average of deaths per million population per day.
Some countries are naturally going to have higher numbers on this metric because they are higher density and have higher regional and international connectedness.

But, FWIW, within statistical noise Sweden and the UK have had very comparable figures, on the same gentle downtrend, since about May 9.
The figures at the moment are 4.85 and 4.88.
In that narrow sense, Sweden's situation is not remarkable.

The figures for Canada and the US are around 2/3 as high as Sweden/UK, flattish for the last week.
Canada seems to be on a slight up trend.
Figures at the moment 3.14 and 2.86.

The figures for Italy, France, and (especially) Germany are around half the North American levels and still falling.
All three countries have been on long downtrends since about April 21 when Germany peaked last, and lowest, of those three.
Germany is very low at 0.34, France low at 0.90, and Italy at 1.36.

As a crude rule of thumb, a figure over 4 (give or take) will make it the leading cause of death that week in a rich country, ahead of ischemic heart disease.

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