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What is a case?

Outside of NYC, New Orleans and Detroit, the number of "cases" is rising across the US:

https://www.nytimes.com/interactive/2020/05/06/opinion/coronavirus-deaths-statistics.html

But what is a "case" ? At one point I found a CDC definition; it was clear as mud. Couldn't find it again today. As with any data, definitions are crucial. Much of the world was ignoring deaths in nursing homes, a rather drastic difference that made it hard to compare our numbers to elsewhere. That has since changed. Now, with cases increasing in most areas, what does this actually represent? If these are people with COVID-19 symptoms, that's bad. But if cases include anyone who tests positive for SARS-2 CoV, then the increase could be an artifact of more widespread testing.

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