Post #981: Herd immunity III: Which states are U.K.-COVID-proof

Posted on January 27, 2021

Source:  U.S. National Park Service.

Edit:  Read Post #982 first.

This is a short post for those who have been following along.  If you haven’t been following along, you should probably go back and read the last two posts on herd immunity.

If nothing else, this post illustrates why somebody needs to do this calculation with full accuracy.  Because, when you get down to it, being able to answer the question below, accurately, seems kind of important.

There’s a new, more infectious COVID variant on the loose in the U.S., commonly termed the U.K. variant.  In this post, I’m going to redo the calculation Post #979, substituting an estimate of the U.K. variant’s viral transmission rate for the previously-assumed 3.33 R-nought (R0 ) value for the existing strains of U.S. covid.

The results will tell me whether any U.S. states have enough “herd immunity” to be have COVID new case rates continue to fall, even as the U.K. variant becomes the dominant COVID variant in the U.S.

The U.K COVID variant is rumored to raise the effective viral transmission rate from roughly 1.1 to maybe 1.5.  That means R0 should rise proportionately, or:

  • R0 (U.K.) = 3.33 x (1.5/1.1) =  4.54.

Now plug that into the required-herd-immunity-level equation from Post #979.  Below, 0.53 is the estimate effect of current masking/distancing/restricting actions.  Solve for the effective herd immunity level He that will produce an effective viral transmission rate of 1, with the U.K. variant.

  •  4.54 * (1 – (H + .53 – .H*.53) = 1.0
  • Solve for H
  • H =~ 0.54

Based on this rough calculation, any state where more than 54% of the population is immune will be protected from this new variant by the combined effect of the population (herd) immunity and the continuation of all other existing efforts to disrupt virus transmission (masking/distancing/restricting).

Look back to Post #958 to see a reasonably current list of states by estimated proportion of population that has already been infected.  Although this is a little old, and ignores vaccinations, it gives you a rough cut.

Prior to the onset of vaccinations, just three states exceeded that level.

I hear that North Dakota is nice in the summer.