I would assume that there's nothing that health authorities can do if people don't report their at home positive test. I assume that the omicron wave was waaaaaay bigger than the reported numbers because so many people are doing home tests rather than going to the doc or a testing site. In the small kansas town where my cousin lives the health department a few weeks ago had to run a notice in the newspaper begging people to pick up the phone when they called. That they weren't trying to do anything nefarious, they were just calling to check and see how people were doing. The health department had also completely stopped doing any testing or reporting because the staff are all moonlighters from their day jobs at the hospital who were plenty busy with their day jobs at the time. (they were sending people as far away as denver (200 miles away) because their hospital and every other hospital in the area were overflowing with people seriously ill with covid.)
My anecdotal thoughts on the home covid tests (yes, the government home tests are the same ones you can buy at the drug store) are that they tend to have more false negatives than false positives. I know several people who had them show negative more than once but then tested positive when they went to a medical facility. I don't know anyone that thinks they had a false positive.





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