The number medical doctors and nurses per 1,000 people by country are shown in the chart below from OECD that was published last year. According to OECD, there were 2.64 doctors per 1,000 in 2019 in the US. Austria had the highest at 5.36 followed by Norway. Generally European countries have higher doctor density than the US.
However in terms of number of available nurses, some European countries and the UK fare worse than the US. There were 11.79 nurses per 1,000 in 2020 in the US.
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Source: OECD