My Original Covid "Modeling"

I recently came across some back-of-the-envelope modeling I did early in the Covid ordeal (05/18/2020). Conclusion was that the duration of "Flatten the Curve" was a theoretical minimum of 214 days. I didn't even bother posting it at the time, because it seemed to depressing.

The core assumption underlying the model was that a large percentage of the population was going to get Covid, it was only a question of when (my working figure was 60%). Then the next key metric requiring an assumption was--what proportion of Covid patients would require hospitalization? My guess at the time was 10%. This turned out to be way too high (by a factor ~5X), although per this paper, I think that was a figure that was circulating at the time.

Anyway, from there it was just a matter of calculating how many "inventory turns" of hospital beds would be required to cycle the entire Covid population through, and how long an inventory turn required (on average). My guess for duration (5 days), turned out to be very low, so partially offsets the high guess for proportion of population infected.

Keep in mind that 214 days is the theoretical best. It assumes the rate of Covid sickness is perfectly optimized, never exceeding hospital capacity (which would imply excess deaths), but never leaving any slack (to ensure the shortest possible duration).

Optimization is always hard, but optimizing rate of acquisition of a novel disease is impossible. So the real-world outcome probably would have been both excess deaths, and still a duration of longer than 214 days. That is, if the 10% of Covid patients require hospitalization assumption had been accurate. Thankfully that was not the case.

0.0028	Hospital beds per capita
0.5	% devoted to Covid patients
0.0014	Steady-state hospital beds
0.60	proportion of population who gets Covid
0.10	proportion of sick requiring hospitalization
0.06	Proportion of population requiring hospitalization at some point
42.9	"Turns" of beds, to cover entire hospitalized population
5	Duration of hospitalization
214	Total days required to work through entire population, if curve flattening is perfectly optimal.