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.

Breakthrough Is a Bad Choice of Words

TL;DR: "Breakthrough infections" is a misleading term, let's not use it. Not sure what the ideal term is, maybe post-vax infections.

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I wish we would stop referring to cases where fully vaccinated people get Covid as "breakthrough" infections. That term has strong suggestion that the primary cause of infection is that a variant strain of Covid has become fully vaccine-evasive. 

Variants do muddy the water a bit, but let's set them aside for a moment. No vaccine is 100% effective. The wide range of available Covid vaccines are quite effective, with the predominant ones used in the US, Pfizer and Moderna, being an astonishing 95% efficacious. Which, reminder, means not that 5% of vaccinated people are destined to eventually get Covid; but rather, the incidence of getting Covid will be 95% lower in vaccinated people.

So, variants aside, the efficacy rate indicates that there will always be some fully vaccinated people who get Covid. Why? The vast majority of the time, it is because, for one reason or another, the vaccine did not generate an adequate immune response. Sometimes because the person is already immunocompromised (more likely if elderly, or if on immunosuppressants, or perhaps exposure to a massive viral load), but also sometimes happens for other reasons to younger, healthy people.

My point: in those cases, nothing has been "broken through" by the nasty Covid virus. Rather, there was no strong defense in place, Covid waltzed right into their body. No breaking was required. This no more involves breaking-through than a non-vaccinated, immunologically "naive" person getting Covid.

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Okay, now about the variants. It is true that some of the variants are better able to evade the immune response of vaccinated people. But the immune response in general is not like a levee that is either breached or holds (excellent article from Zeynep that explains this). And the immune response from the vaccines is particularly massive. So while variants to-date may be somewhat more likely to cause a breakthrough post-vax infection, that is incremental--it is not the main explanation, and hence it is misleading to refer to it as a breakthrough phenomenon.

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Another thing that should be emphasized is that even when breakthrough infections occur, the severity is markedly less. Many are entirely asymptomatic, and found only by random testing. Others are very mild. The efficacy of vaccines against severe Covid and death is stunningly high, in the 99+% range. That gets back to the flawed levee analogy, and also maybe the nature of Covid variants, as compared to other things, especially the familiar disease-resistant antibiotics. It it much less all-or-nothing. A person with a weaker response, or a variant that is more vaccine-evasive, usually involves far less risk of a dire outcome than for an unvaccinated person.

So variants are worrisome, but not cause for panic. Of course, the more people that get vaccinated, the less change for variants to emerge. 

In the meantime, let's stop referring to post-vax infections are "breakthrough".

The Equilibrium Principle

Covid stats are through the roof. Sad, but predictable, if one understands equilibrium states. The average person, I think, isn't equipped to have a mental model of how a highly contagious disease works. The USA went into "lockdown" in March and April, just in time to prevent exponential spread from getting out of control. It worked. The curve was flattened.

Then we came out of lockdown, with mixed results. Overall though, while Covid numbers were bad enough, they remained well short of exponential. Mask usage--which has vastly out-performed expectations--very likely helped, as did good weather.

As the months wore on, a combination of complacency and fatigue set in. Complacency, that Covid, while still a problem, seemed to be bubbling along at a bad but tolerable level. Fatigue, for all forms of social isolation, including mask-wearing.

And then in the blink of an eye, the combination of change in weather, resumption of college, and the fatigue has got us in the worst state yet. 2 months ago, my pessimistic scenario was that we might be in 70% as bad a situation 2 months from now, in the depths of winter. Given that in many places we are close to maxing out ICU capacity, I can hardly bear to think of how bad it could be come January.

Covid Questions I Would Like to See Answered

Why Haven't There Been More Outbreaks at Health Clubs?

How Likely Is It That a Sleeping Partner Will Catch Covid?

Does CPAP Help Prevent Getting Covid?

What Is the Equation for Viral Load Over Time?