Delta Surge Progression and Forecasting

After what unfolded in India in February and into April, I began closely watching how the frequency of the Delta (Δ) variant grew in different countries, especially the UK. Covariants.org has been scraping viral genetic sequencing data for some months now and charts the frequencies of different variants in different countries and, in the case of the Unitied States (US) and Switzerland, smaller political subdivisions. Frequency is the fraction of all COVID cases that are attributed to a specific variant. I was concerned when Delta appeared to outcompete Alpha (A) in India (Deltas frequency began to push out Alpha, implying it is either more contagious or able to evade immune response generated by infection with other variants and vaccination, or both). What I did not know is how Delta stacked up against vaccines since India had a very low vaccination rate.

There is a lot more mixing between the United Kingdom (UK) and India (both members of the Commonwealth of Nations) so the UK saw Delta beginning to spread a lot earlier than in the US. With similar vaccination rates I believe the UK can be a good predictor of how Delta might impact the United States. Here I look at England’s case data. (England is a political sub-divsion of the UK containing about 80% of the UK’s total population.)

England as a Predictor

A few weeks ago, when it became clear California’s new cases were creeping up, I noted that the frequency of Delta when England’s new cases turned up was about the same as it was in California when its cases turned up. In both places this happened when Delta frequency was about 0.5 or half of all new COVID cases. This felt like confirmation that England could be a good model. Spend some time looking a the plots at Covariants.org. The progression of Delta frequency is pretty universal from country to country, roughly doubling every two weeks when the fraction is < 0.5 .

As the weeks progressed, I began plotting England’s new case data with California’s. I am interested in California because I live here, but also because it was one of the first parts of the US where Delta got a toehold, and has similar vaccination rates to England.

Note: In late May and late June there are odd reporting glitches in the California data set, with days of 0 new cases and others with tens of thousands. Here the trailing averages do not track suspect days. This helped make the plot more readable, but as you can see that correction was not perfect.

On a logarithmic plot it is easier to see exponential trends. (On a log plot in the vertical axis there is an even amount of spacing between 1 and 10, 10 and 100 and 100 and 1000, instead of say 1 and 2, 2 and 3, and 3 and 4). Case decline and increase curves often have had fairly flat slopes on log plots throughout the pandemic. The slope scales with number of new cases each infected person causes. (If someone can point to good youtube primer on this please let me know and I will link it here) . This number is sometimes called the reproduction rate or R0. When each infected person generates on average more than 1 new case the number of new cases goes up over time, exponentially. (100 cases becomes 200 in a week, 200 becomes 400 the next week, etc.). When it is less than 1, new cases decline exponentially (400 becomes 200 becomes 100 becomes 50, etc. ) The steepness of the slope is proportional to what this number is. Typically during the pandemic in different locations I have seen this number between 0.7 and 1.5 with brief excursions out of that range.

I was impressed to see how similar California’s slope was to England’s on the log plot. This means, under the influence of Delta, and each area’s amount of people gathering, precautions taken and the impact of vaccination, the growth rates have been about the same. This is more confirmation that England can be a good predictor for California.

Forecasting

Recently, cases in England began to turn downwards. The plot above is a 7 day trailing average, so arguably, the downturn began three or four days sooner than the peak of the curve. Now that the trend has been ongoing for a good week or more, it looks real, and not like a reporting fluke. Why it turned down is not known. I know social distancing rules did not tighten (in fact, they loosened on July 19th, though that impact could not possibly be seen in case numbers for several more days after and would just be showing up now). My hypothesis is Delta infections have gone underreported and enough people have been infected so currently infected people don’t encounter enough susceptible people to keep that reproduction rate bigger than 1. The turn in England happened about 65 days after hitting a Delta frequency of 0.5 (50% of new cases). Those are the facts. What follows is speculative.

65 days after California hit 50% Delta is August 20th. I predict California’s 7 day trailing average will crest around then, with new cases peaking about a 1000 per million people, or about 40,000 new cases a day. For comparison, this is about where daily new cases peaked last December. This time, hospitalizations should be considerably lower because vaccinations do do a pretty darn good job of keeping people out of hospitals. Maybe it will be 50%-60% lower than it was in December.

In places with lower vaccination rates than California around the US, that 65 day span could take a little longer, but with vaccinated people apparently spreading it just as effectively as unvaccinated folks (they just don’t become as ill) I believe 65 days will be pretty universal. When it ends will vary from location to location depending on when Delta got a toehold. (For instance, that is about the span of India’s surge. Not identical, but close. Additional confirmation…and in hindsight that vaccination does not slow Delta transmission notably, it only diminishes how severely ill an infected person becomes). The areas with lower vaccination rates will see a heavier load on their hospitals, but I believe the span of this horrific climb in cases will be similar.

This illustrates roughly the same span of time between the pre-delta minimum and the peak in the UK. As you look at case rates here, note that India probably has a severe under-reporting problem. Th

Florida is about 2 weeks behind California in its journey. They can expect cases to keep climbing at this breakneck rate into early September. The curve may not keep the same slope, because already there are reports of people having to wait in long lines for tests. More cases will go undetected and unreported. Hospitalization won’t though, unless it gets so bad that people start dying at home because there are no beds. My home state of NC is about a week behind California. Check out Covariants.org to see what might happen where you are, but remember if the numbers of total sequences cases are low (say less than 100) the frequency value is going to have a large uncertainty.

How Certain is 65 days?

There is nothing magical about 65 days and there are uncertainties in figuring out delta frequency, so the specific timeframe might be off. I could also be dead wrong in this simple analysis. Delta is so aggressive though, I will be surprised if this is off by more than a week.

The Netherlands had an apparent surge and peak that is a lot less than 65 days. The Netherlands is a different place with different attitudes towards lockdowns. In the midst of their surge, their government reinstated a work from home order and placed restictions on bars, restaurants and clubs. In the US and UK that has not been done, and if it was, it probably would not be well followed at this point. Folks row in the same direction more in the Netherlands. Not a judgement, just a fact. If I am right, their Delta period will be longer. They won’t have fewer cases per capita total, just a longer flatter curve. Another explanation is they had much higher case rates on average than the UK over the past 6 months. Perhaps a significant fraction of their people have cross immunity from Alpha infections that occurred during that period.

65 days also is not the end, it is only the peak of the surge and it will take time after that for cases to die down. Balance any optimism with realism (re: the Stockdale Paradox) This 65 day span could be altered too, for instance if a country goes from free-for-all mixing to near complete lockdown (and has a compliant population) or vice versa the shape and width of the curve will change. What we are seeing here is that the precautions that “flattened the curve” a year ago have a lot less of an impact in the Delta driven phase of the pandemic. Right now, Delta is in the driver’s seat.

There is a big push for vaccination now. People are becoming afraid and those who had not gotten around to it but were willing are getting it done. The sad thing is, with 6–8 weeks between the first shot and full immunity, it will help in saving lives more on the downslope of the surge than at the peak. It will help against future surprises SARS-CoV-2 might send our way so it is a good that more are getting it.