Post #1340: COVID-19 trend to 12/6/2021, 15% per week

Posted on December 7, 2021


At this point, the data reporting issues from Thanksgiving should be in the past.

Every region of the country now shows an upturn in cases.  Best guess — via connect-the-dots, below — is that new COVID-19 cases are now rising about 15 percent per week, on average, in the U.S.

Data source for this and other graphs of new case counts:  Calculated from The New York Times. (2021). Coronavirus (Covid-19) Data in the United States. Retrieved 12/4/2021, from”  The NY Times U.S. tracking page may be found at

There’s obviously some uncertainty in that figure.

For one thing, the CDC’s data on hospitalizations show slower growth.  The most recent figures there show a roughly 9 percent per week growth rate.

Source:  Calculated from CDC COVID data tracker, accessed 12/7/2021

So the trend is up, but exactly how much is not quite clear (and/or cases continue to shift toward younger individuals who are less likely to require hospitalization).  That said, if I put the first and second pandemic years on the same graph, that 15% rate of growth is in the same ballpark as last year’s winter wave.  Maybe a little slower.

So, for the post-Thanksgiving period, it looks like we’re on roughly the same track as last year’s winter wave, just a bit later.

It’s not an exact repeat.  Last year, the Midwest and Mountain states were leaders on the upslope of the wave.  This year, it’s more like Midwest and Northeast.  But so far, the U.S. average seems to be running just a few weeks behind last year’s numbers.

A crude Omicron extras for experts.

An Omicron fun fact is that the current observed viral replication rate in South Africa is about 2.0.  That is, the number of cases doubles with each new generation of infected individuals.  (Equivalently, on average, each infected person goes on to infect two others.)  And that’s with Omicron accounting for about 75% of new cases as of the most recent data.

I’m now going to do an extremely crude what-if calculation for the U.S.  What if we were to substitute Omicron for Delta, right now, in the U.S.?  What would happen to our current 15% per week growth rate?

(This calculation is not merely crude, but is downright wrong, in that I’m just going to pretend that each generation of new COVID-19 infections takes exactly one week.  The generation length is actually shorted than that — something like 4.5 days.  That’s a material difference, but given how crude these guesses are, for the sake of simplicity, I’m just going to pretend that the weekly growth rate is the same as the viral replication rate.)

So, let me assume that Omicron and Delta are identical, except that Omicron is twice as infectious.  And let me further assume (contrary to fact) that it takes one week to generate each new set of infections.

Taking the standard simple equation for growth of cases in a pandemic, what would happen to the current 15% growth rate, if we were instantaneously to swap Omicron for Delta?

The standard simple equation looks like this:

  • R-observed = R-nought x (1 – fraction of infections stopped).

The observed rate of case growth is the R-nought (no-precautions-taken, no-immunity-present) rate of growth, less the number of infections you manage to interrupt with your precautions such as vaccination, masks, and other forms of COVID hygiene.

Substituting numerical estimates for those factors:

  • 1.15              = 5 x (1 – fraction of infections stopped)

The 1.15 above is our current 15%/week new case growth rate.  And the 5 is our best estimate of R-nought for Delta.

Doing the algebra, you then estimate that:

  • Fraction of infections stopped = (1 – 1.15/5) = 77%.

Between immunity (prior infections and vaccinations), and our residual behaviors to prevent COVID spread (masks, distancing), we manage to interrupt 77% of the chains of infection that would otherwise take place.  That’s how we manage to get a mere 15%/week case growth rate, out of a virus that would normally (no precautions, no immunity) generate a far higher growth in new cases.

Now for the what-if.  What if we continue to interrupt 77% of infections, but substitute Omicron’s R-nought of (say) 10, instead of Delta’s 5?  (See prior post for where the estimate of 10 comes from.)

  • R-observed (Omicron) = 10*(1 – .77) = 2.3

In other words, each week, the number of new cases would go up by a factor of 2.3.  (Instead of a factor of 1.15, as we currently observe with Delta).  We’d be seeing something similar to what they’re observing now in South Africa.  Every week, you’d see weekly new cases more-than-double.

This is obviously crude, and there are a lot of caveats, and in fact, the R-nought estimate for Omicron may be somewhat dependent on the exact situation in South Africa, because that’s the only place where that has been measured.

But putting all that aside, I want there to be a few simple takeaways from this what-if calculation.

1:  What’s happening in South Africa really can’t be wished away as some consequence of their particular situation.  If you’re of a mind to say “well, that can’t happen here”, think again.   It’s just a matter of arithmetic.  If we faced the same virus they are now facing, we’d see spread similar to what they’re seeing.

2:  This is a highly “leveraged” situation.  If you naively thought that doubling the R-nought (infectiousness) of the virus would double the weekly case growth, you were wrong.   What drives the new infections is that small difference between R-nought, and the fraction of infections blocked via immunity and hygiene.  Doubling the R-nought (from Delta to Omicron) does NOT take new case increase from 15% to 30%.  It takes weekly new case growth from 15% to 130%.

I hope this exercise helps you grasp why Omicron has set off alarm bells.

People who say that the world’s experts are overreacting haven’t bothered to do the math.  There are caveats galore.  And maybe Omicron isn’t as virulent as Delta.  But you’d be crazy not to take this seriously.