# Post #799: Some simple arithmetic on herd immunity

Posted on September 2, 2020

This is just another basic math problem. Because people seem to keep forgetting the diagram above.

The point is, if you were to spread COVID-19 in Virginia as fast as possible, 13 times faster than it’s spreading now in Virginia, vastly faster than we have seen in any other state, subject only to the constraint that you don’t run out of ICU beds, the simple arithmetic says it would take a year and three months to achieve herd immunity in Virginia.

Which, I hope goes without saying, is far beyond when we can plausibly expect to have a vaccine.

This is really just a way of re-emphasizing the related calculation I did back in Post #681 (4/4/2020).  That’s a different and more realistic calculation, and there I still came up with something like two years.

“Herd immunity” seems to be getting a lot of attention from some White House advisors.  My question is, can anyone in the White House be bothered to do even the simplest bit of grade-school arithmetic, before we end up that that as our main approach to dealing with the pandemic.

Details follow.

Let’s say that you were bound and determined to pursue a strategy of “herd immunity” here in  Virginia.  But in a somewhat humane way.  You’d arrange to have COVID-19 rip through the population as fast as possible.  Subject to just one constraint:  Not running out of any critical hospital resource.

I’ll call that the “no corpses in reefers” clause.

How long would it take?

If you look at Virginia hospital data, it appears that the ICU beds are the binding constraint.  Including newly-added surge capacity, there are just 3500 empty ICU beds.  (And if you don’t include surge capacity, it’s far fewer).

Let me make the heroic assumption that those are all staffed beds.  Because I suspect that staffing is itself more of a constraint than the beds are.  But let me just assume that away.

Right now, at our current rate of 12 new cases/ 100K population/ day, there are 266 COVID-19 patients in ICU beds.

Roughly how much higher could that daily infection rate go before we’d fill all the empty ICU beds?  Doing the long division, if ICU beds are the constraint, we could, in theory, have 13 times the current infection rate (3500 available beds/266 used at the current infection rate) before we’d keep all those ICU beds filled with COVID-19 patients.

That would mean a diagnosed infection rate of 156 / 100K / day.  (13 times our current 12 / 100k/ day).  Assuming no other constraints.  And ignoring the fact that this is off-the-charts.  Many other states have come close to hitting their hospital limits at a tiny fraction of that rate.

But, for the sake of argument, let’s just assume that “capacity” in Virigina is reached at 13 times the current rate, or 156 new cases/ 100K population / day.  And that, somehow, we could goad the population into getting infected at that rate.

Question:  How long would it take use to achieve “herd immunity”, defined has having 70% or more recovered from COVID-19?  Under that ludicrously unrealistically high rate of infection.  But ignoring the fact that there are probably several un-diagnosed cases from every one that is diagnosed.

Answer:  (70% x 100,000 / 156 = ) 448 days, or about a year and three months from now.  Well beyond anybody’s expectation of when we’ll have vaccines available.

The point is, unless you want to stack bodies up in trailers, “herd immunity” isn’t a strategy as much as it is a fantasy.  Even pedal-to-the-metal, it would take longer than a strategy of distributing a vaccine.

But what’s most annoying is that it’s a fantasy pushed by people who cannot be bothered to do simple grade-school arithmetic.  Before attempting to shape US health care policy.

Back when I worked for a US legislative-branch health policy agency (MedPAC), a colleague of mine had a name for things like this:  Policy malpractice.  If a physician screws something up in a negligent manner, you can sue them.  But if a federal official promotes negligently promotes a health care policy that’s obviously unworkable, you just have to live with it.  Or die from it.  It’s a shame that you can’t sue them for policy malpractice.