Understanding the math of #Covid

I have spent a lot of time looking at the math of #covid. I try to ignore both the unrestrained panic as well as the comments of the cavalier and focus just on the math. The math is both frightening and complicated. It is frightening because the worst case scenario present in the numbers is significant. It’s not apocalyptic, but it has a lot of potential to be bad. It is complicated because it’s doing algebra with a large number of variables.

Why Clarity Matters

To start, let’s understand two key terms: Case Fatality Rate (CFR) and Infection Fatality Rate (IFR). CFR is the number of deaths relative to the number of known cases. Currently that number sits at 3.5% (111,363 known cases and 3,892 deaths). IFR is the number of deaths relative to the number of people infected. That number is currently unknown. We simply have no idea how many people are infected.

This becomes important when you hear public officials say “we think the fatality rate is closer to 1%”. Some have gone so far as to say the number is closer to a really bad flu at .1% to .17%. The assumption present in this is that a great number of people have no idea they are infected. They are, in essence, arguing the IFR is actually 1, despite the CFR undeniably being 3.5.

Here is why that matters. If you have ever done accounting, you know that you need to reflect any changes on both sides of the ledger. If you suggest that the CFR is off by a multiple of 3.4, and the IFR is actually 1, you have to assume that the number of infected is significantly higher than the number of known cases.

To reach an IFR of 1, the total number of cases in the world must actually be around 379,000. If you believe the IFR is in the range of .17, then the CFR must be off by a multiple of twenty (or 2.2 million infections).

The reality is, we have no idea what the infection rate is. WHO’s Bruce Aylward says their assumption is that the number of known cases is accurate as an expression of infection rate. He notes that those who test positive asymptomatically typically show symptoms within a few days. So they question whether there really is a great unknown horde of infected. As a result, the WHO is operating under the theory that 3.5% is pretty close to correct.

However, if public figures are going to quote fatality rates, then they should be obligated to report the number of suspected infections that make them true. Clarity matters. If you believe the IFR is 1, then you must necessarily also suggested the number of infections is close to 400,000. If you suggest it is .17, they should be required to report the number of suspected infections is more than 2 million.

You simply can’t have it both ways; claiming a fatality rate lower than what is observable without acknowledging the substantial increase in infection rate that requires.

So Why Does This Matter?

You may have heard the statistic that the infection rate is doubling every six days. If you start with one infection in China first reported at the end of December and double that every six days, you end up with ~96 days to get to more than 100k infections. We are currently around day 70.

To get to 400,000 cases would require almost 114 days, or almost one and a half times as long as the virus has been circulating. To get to 2.2 million would require 129 days, or almost twice as long.

So accepting the unseen infection theory of the fatality rate means also accepting that the disease is traveling one and a half to two times faster than we are seeing.

That would indicate that the disease is much more transmissible than current cases suggest, and that the r-0 value is greater than estimated. In either case, the ability to contain the disease is greatly impacted by those assumptions. The ability for the public to respond is greatly impacted by a faulty understanding of the level of infection.

Disclaimer: I am not a medical professional and certainly not a virologist or epidemiologist. My interest in infection rates and disease spread comes from a simple fascination with disease outbreaks that I have had since childhood. As a political communications professional, I understand the desire to minimize the public impact of panic. It is, however, critical that our public officials be held to account when they statistically mix apples and oranges and end up misleading the public as I think they have done in the #covid response. As such, if you take issue with my statements, I encourage you to share where you think they are wrong.