First, simply put, what is a "case"? There was a great discussion and article on this topic yesterday. Basically, previously, "a ‘case’ represents someone with symptoms, usually severe symptoms, usually severe enough to be admitted to hospital...However, now we stick a swab up someone’s nose, who feels completely well, or very mildly ill. We find that they have some COVID particles lodged up there, and we call them a case of COVID...A symptomless, or even mildly symptomatic positive swab is not a case. Never, in recorded history, has this been true. However, now we have an almost unquestioned acceptance that a positive swab represents a case of COVID."
To be fair, the CDC historically estimated influenza "cases" because not everyone with severe influenza goes to the doctor or hospital. But now, if Jonnny goes to a kegger at college and feels winded and has lost his sense of taste, he gets tested at the clinic and BAM! he's a COVID19 case, even though Johnny is still going to hybrid class and playing Fortnight from 1-5am.
This leads to the calculation problem. What do we want to estimate? The mild non-"case" cases or the "cases" in the traditional sense? We can try to do a decent job on both, though the former is easier than the latter. In fact, we may simply surrender on the mild non-"case" cases and declare that the official tally is that number though I believe that reported value is light because many people who got COVID19 may not have bothered getting tested or tests weren't available.
To get to a reasonable, traditional "case" estimate, we can take a page out of the CDC's playbook and look at "surveillance data, outbreak field investigations, and proportions of people seeking health care from survey results" to get to a legit traditional COVID19 "case" value. There are probably newer sources of data into which we can tap, including Mobil phone tracking data (I'm not taking about monitoring individuals, just traffic flow around clinics and hospitals etc), to better refine the prior listed methodological values.
My own work on fatalities (which is rudimentary) points to number about 1/3 of the reported total in the US. Your mileage may vary.
Btw, I don't believe this is a mild flu...this is a nasty virus that kills you at least four ways. I know of people who've had it and recovered easily and died miserably from it. I also don't believe vaporizing the service economy or shutting down the nation was wise.
I guess when this is over, on Nov. 4, we may be able to do that. Thanks for your time and effort, good people.