Validity of Coronavirus Curves - Are we using the correct baseline?

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For most analysis (models), are we inaccurately assuming that the newly reported cases are the number of actual new cases? Could this exponentially growing number just be a function of the way testing is being rolled out and not represent the actual growth rate of the virus? Should we be basing the growth rate off of hospitalizations instead?

I just have to ask myself if our testing capability is expanding exponentially and since we can see symptoms for up to 12 days in these people that we are not making the curve look exponential when it may not really be doing that?

For my example, if my state currently has 50K with covid19 and lets say it grows to 60K over the next week. If testing is rolled out with exponentially more tests each day, wouldn't that appear there are exponentially new cases but in reality it's grown on a flat linear line?

Should we use the hospitalization curve since that is the capacity we care about anyway?