Quarantine Day 29: Occam’s Razor Applied to COVID Models

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Today the head of the CDC, Dr. Robert Redfield, announced the virus has stabilized. He cautioned however, that the virus is still expanding and that the apex has not yet been reached. Let’s explore Dr. Redfield’s statement to better understand what he means when he says the virus is expanding. If the virus is expanding, then the rate of growth for either infections of death is increasing.

Applying our simple exponential formula, f(x) = a^x, if the virus is expanding, then variable a, should increase over time. The apex that Dr. Redfield referred to occurs when the rate of change for the virus stops increasing. In absolute terms the apex occurs at the highest point in the rate of expansion after which, the expansion rate contracts. In reality, the apex can be over a period of time where the infection/death rate is nearly constant (with small variation).

If the virus follows what is called a “bell shaped” curve, then the rate of contraction as the virus recedes will mirror the rate of expansion the virus followed on its way up to the apex. In other words, if the number of people in the US who got infected 10 days before the apex was say 20,00, then the number of people who get infected 10 days after the apex will also be 20,000. Many things in nature follow a bell shaped curve, but it’s yet to be determined if COVID will.

Reaching the apex does not mean we’re out of the fire, it just means we’ve slowed the rate at which we’re adding fuel to the fire. If the apex is reached when 20,000 people a day get infected, then for the apex period, +-20,000 a day will continue to get infected. And then during the contraction period, just as it took several weeks to ramp up to the apex, it will take several weeks to ramp back down and if we’re not vigilant, we could restart expansion; something I have to keep reminding my kids.

The apex is an important milestone because it signals when the worst is behind us and strategies can be modified.

Dr. Redfield asserted that 1) the virus continues to expand and b) the apex has not been reached. I however assert the virus has been contracting for several days. To demonstrate, we can again call on our virus modeling formula and apply it to Dr. Redfield’s own CDC data.

But wait you say, our model is so simple while federal and academic models are much more complicated and take into account way more information. Well you’re right, federal and academic models are substantially more complicated but in science, that’s not always a good thing. There’s an important axiom in science called Occam’s Razor, which in one of its many forms states

“given a set of explanations for an event, the simplest one is most likely correct.”

Our simple formula is what is referred to as a “first principles” model. This means it uses a basic formulation with minimal assumptions or reliance on extraneous information. As validation of Occam’s Razor applied to our first principles formula, our April 2^nd projection of the US death count by April 14^th appears to have a forecasting error of 30%, while federal and academic models appear have a forecasting error of 964% (determined using Mean Absolute Percent method of forecast error analysis).

An equally salient point as it pertains to Occam’s Razor, is that our first principles formulation relies exclusively on CDC data while federal and academic models rely on that same data plus a plethora of assumptions and extraneous information. The rub however, is that the CDC data has all the information needed about virus behavior already embedded in it. In that sense, our formulation has all the relevant information needed to make a first principles analysis. I get the feeling federal and academic modelers don’t understand this.

It is my contention that CDC director Dr. Redfield’s statements today are wrong. If you look at the table above and the corresponding graph, which are drawn from CDC data, you see that the national value for variable a, in f(x) = a^x, has been declining since March 24th. In other words, the virus rate of growth has been contracting and that can only happen if the apex has already been reached.

Tomorrow is April 14th, the day projected by federal and academic models when the apex would be reached. I anticipate that tomorrow federal and academic experts will tout their modeling prowess by proclaiming the apex has been reached as they projected, and that the virus is now in decline; two things we’ve know for quite some time now.