COVID-19 Delta Variant – A Real-Life Horror Story in Numbers.

Existing vaccines won’t stop the Delta variant spreading, and here’s why.

While existing COVID-19 vaccines will reduce hospitalisations and save many lives, they are not effective enough against the Delta variant to stop it spreading.

The facts:

The Delta variant is at least twice as infectious as the original COVID-19 variant, with an R0 of at least 5.0, and possibly as high as 8.0. Vaccinations, borders, and the Delta variant

Studies show the mRNA COVID-19 vaccines seem to be the most effective, and the Pfizer vaccine seems to be the most effective of them, edging out the Moderna vaccine by a slim margin. For this reason, and the lack of data on the Moderna vaccine’s effectiveness against the Delta variant, I’m using the Pfizer vaccine for my calculations.

While preliminary findings of a Scottish study published in The Lancet last month (June 2021) found that the Pfizer vaccine provided 79% protection against all infections from the Delta variant, this month the Israeli Government reported that the Pfizer vaccine is only 64% effective at preventing Delta variant infections. Israel sees drop in Pfizer Covid vaccine protection, still strong in severe illness

The Maths:

Even with best case assumptions of R0 = 5.0, 79% Vaccine Efficacy and 100% vaccination, the Delta variant’s transmission rate would be 1.05 (21% of 5.0), which is over the R0 < 1 threshold for herd immunity, so any outbreak would continue to grow and spread (the 21% is the complement of the 79% vaccine efficacy – i.e. 100% - 79%, being the proportion of people that the vaccine doesn’t protect from infection).

But wait, it gets even scarier:

In practice, 100% vaccination is unachievable, so the rate of transmission would be even higher. For example, with an 85% vaccination rate, the 79% is replaced by (79% x 85% = 67.15%), giving a transmission rate of 1.6425 (32.85% of 5.0), meaning the outbreak would spread even faster.

If, as seems likely, the vaccine is only 64% effective, then that 85% vaccination rate gives us an effectiveness of 54.4% (64% x 85%), which gives a transmission rate of 2.28 (45.6% of 5.0).

A transmission rate of 2.28 is getting close to the original variant’s transmission rate without vaccines, and it would only take the vaccination rate to be a bit lower (< 78.125%), or the Delta variant’s actual transmission rate to be 5.5, which is well within the range of probable values, for the Delta variant to spread faster in the vaccinated population than the original COVID-19 variant spread in an unvaccinated population, and while vaccinations would reduce the death rate we would still be looking at significant mortality.

Some Scary Speculative Guesswork:

The Alpha variant increased both hospitalisation and R0 by approximately the same amount. If this is also true of the Delta variant, that would give it an R0 (transmissibility) around 7.4, almost three times that of the original COVID-19. While this is guesswork, an R0 of 7.4 is within the range of values considered likely for the Delta variant.

At this R0 and a vaccine effectiveness of 79%, at a vaccination rate of 83.8% the virus would spread faster than the original COVID-19 did without vaccinations.

With such an R0, to achieve herd immunity by vaccination alone:

• would be impossible at anything less than 86.48% vaccine effectiveness. 
• would be impossible at anything less than 86.48% vaccination rate.
• would require a vaccination rate above 91.5% at 94.5% vaccine effectiveness, or
• would require a vaccination rate above 96% at 90% vaccine effectiveness, or
• would require a vaccine effectiveness above 96% at a 90% vaccination rate.

In practice, even the theoretically possible herd immunity scenarios above seem unlikely to be achievable even with an updated vaccine tailored to the Delta variant.

How Deadly?

The following are only estimates, and are based on limited data, so may be inaccurate.

Published comparisons with the Alpha variant, combined with data about the Alpha variant, suggest hospitalisation rates around three times higher than the original variant, with death rates likely to be similarly higher. And of course, with higher hospitalisation rates we can reasonably also expect higher rates of Long Covid (for those who survive).

The good news is that apparently full vaccination with the Pfizer vaccine is 93%-96% effective in preventing severe disease and hospitalizations, and even the AstraZeneca vaccine is up to 92% effective. Israel sees drop in Pfizer Covid vaccine protection, still strong in severe illness  

For exposed people, I estimate mortality if vaccinated to be between 0.24% and 0.95%, and if unvaccinated to be between 6% and 13.5%, with overall average mortality at 85% Pfizer vaccination rate to be between 1.10% and 2.83%, where I define exposed as sufficiently exposed to cause infection if unvaccinated. Actual average population mortality would be lower, as even in an uncontrolled epidemic with no other COVID-19 specific precautions not everyone will qualify as exposed, due to variations in individual susceptibility and circumstances. However due to the highly contagious nature of the Delta variant it’s possible that if other precautions are not taken during an epidemic more than 50% of the population could be sufficiently exposed to cause infection if unvaccinated. Additionally, with an 85% vaccination rate, a significant proportion of unvaccinated people would be vulnerable people with co-morbidities who couldn't be vaccinated for health reasons, further raising the unvaccinated persons mortality, and thus the overall mortality.

The tedious stuff:

The Delta variant apparently requires hospitalisation 85% (95% CI 1.39–2.47) more often than the Alpha variant (SARS-CoV-2 Delta VOC in Scotland: demographics, risk of hospital admission, and vaccine effectiveness), which in turn has both hospitalisation and death rates 60% (95% CI 1.42–1.82) higher than the original variant (SARS-CoV-2 Alpha variant). This suggests hospitalisation and probably death rates around three times higher than the original variant, however the wide Confidence Intervals (CI) introduce a lot of uncertainty, so that hospitalisation rates could be anything from 1.97 to 4.50 times higher than the original variant, with death rates likely to be similarly higher.

Posted by Andrew the Longwinded 14 July 2021.