The link below gives a good explanation about why it is important that the positivity rate is low. First, here is my take. (Keep in mind that I’m not a statistician, though I used to play one when I taught a senior/graduate level course in it, but it was not really statistics; it was the math behind the statistics.)
Here we go.
At times it is hard for me to tell the difference between a cold and allergies. The symptoms are the same early on. Suppose that from every 100 people who have those symptoms in May, 20 have a cold. You know that from diagnosing thousands and thousand of people.
Now, suppose that I tell you that in a big city, out of all of the tests I did to see who had a cold, 50% actually had a cold. You would be correct to wonder if something was wrong. It might be that I only had 20 tests, even though 100 people had the symptoms. Since I could only test 20 of them, I would want to be careful so I could find as many as I could that had a cold (because they are contagious). So I would limit my tests to those who have many symptoms that look like a cold, not just sneezing, say. So, because I only tested people with lots of symptoms, I found 10 people (50% of those tested) that really had colds and I would tell them to stay home. BUT had I been able to test all 100 with any reasonable symptoms, I would have found 20 total people with colds (the 20% number we would expect to find). So, since I only had 20 tests, there are 10 people running around with colds giving their cold to others – in other words community spread that I could have stopped if I had the 100 tests that I needed. That is why a high positivity rate is bad and a sure sign of community spread.
For Covid-19, statistics show that, in order to stop growing community spread, you need a positivity rate of 5% or less. You still miss cases, but not enough to let the virus spread in a big way.
Here is the link
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