The new variant, R, and why it’s more complicated than that
There’s increasing consensus that the new B 1.1.7 variants* of the Covid virus really are importantly more transmissible than the previous versions, which then raises the question of whether NZ-style lockdowns will still work. You’ll see people trying to do simple arithmetic on the basic reproduction number, R, to work this out, but it’s more complicated than that.
In a very simple epidemic model, the number of people infected by a case is the number of people they come into contact with, multiplied by the probability that they infect each one. You would think of interventions such as lockdown as affecting the first factor and differences in the virus as affecting the second. In this model, if a new variant has R about 1.3 times higher than the existing virus, for the same contact rate, it is increasing the infection probability by 30%. If lockdown decreases R for the old virus from, say, 2.5 to 0.8, then it would decrease it from 2.5×1.3 to 0.8×1.3 for the new virus. That’s not a completely useless way to think, but it’s nowhere near good enough for government work.
The issue is that interventions don’t affect all transmission equally. Imagine we had the impossible perfect lockdown, so you only came into contact with people in your bubble — any essential shopping was done by perfect zero-contact delivery or something. Obviously, the virus would not spread between bubbles; that’s exactly what we’re assuming. However, the effective reproduction number would still be greater than 1 initially, because the virus would spread within bubbles. A combination of testing and isolation and just running out of susceptible people in affected bubbles would get the effective reproduction number down near zero eventually, but there would never have been any between-bubble spread.
In the real world, or even in New Zealand, we won’t have the impossible perfect lockdown. But back in April alert level 4 reduced between-bubble transmission a lot, and it will be combined with now knowing about masks and airborne transmission plus now having much more testing capacity than in April plus now having faster tracing than in April. Is that enough? Well, you need a more sophisticated model to tell you, one that’s between our two simple extremes of no population structure and perfect lockdown. We have those models, and what I’m hearing is that level 4 lockdown would work, but it’s not clear that level 3 would work.
There are other related questions where you need a model rather than simple intuition. For example, is the new variant more likely than the old ones to appear with no obvious contact to the border (as in August), making a lockdown more likely? Apparently, the answer is “yes, much more likely”.
It’s amazing how far you can get with unstructured differential-equation models for epidemics, and they are still valuable, but for some questions you need to model something closer to the real population, and it’s harder and takes longer and the results don’t necessarily have a simple intuitive explanation.
* if you don’t say “China virus”, you probably shouldn’t be saying “UK strain”
Thomas Lumley (@tslumley) is Professor of Biostatistics at the University of Auckland. His research interests include semiparametric models, survey sampling, statistical computing, foundations of statistics, and whatever methodological problems his medical collaborators come up with. He also blogs at Biased and Inefficient See all posts by Thomas Lumley »
The original R value was 3.5. The new variant is 70% more transmissible so the new R value is 6.0. The Oxford vaccine is 60% effective so if everyone is vaccinated with it then the new R value becomes 2.4. It’s still greater than 1 so the vaccine won’t work.
That might be a useless way to think but it does convey the gist of the way calculations should be done.
3 years ago
1.That’s higher than most estimates.
2. No, what’s being quoted is an absolute increase of 0.7 in R, not a factor of 1.7
3. We have *literally no data* on how any of the vaccines affect secondary transmission, which I why I didn’t write about the effect on vaccination.
3 years ago
It occurs to me that you might have thought I was referring to the ANZ Society for Immunology and its call to halt the AstraZeneca vaccine rollout in Australia.
I wasn’t. If I had been, I would have said so, and linked, and so on.
3 years ago
No, I was just playing with numbers. And I completely made up the number on secondary transmission. I didn’t realise that the Australian discussion was going on.
I wonder if it is possible to measure how any of the vaccines affect secondary transmission from field data without doing trials. I guess we will find out when everyone has been vaccinated and the virus is still going around.
3 years ago
The estimated new variant is BETWEEN 0.4 and 0.7 more transmissible. For its usual reasons the media report the highest number. The numbers are probably specific to the UK.
‘Using a variety of statistical approaches, the team evaluated the relationship between transmission and the frequency of the new variant across regions in the UK over time.
Using whole genome prevalence of different genetic variants through time and phylodynamic modelling (dynamics of epidemiological and evolutionary processes), researchers show that this variant is growing rapidly.”
https://www.imperial.ac.uk/news/211793/new-covid19-variant-growing-rapidly-england/
Amazing the ability to meld together new techniques rapidly in a fast changing situation that has real consequences.
Weird that some people are trying to ‘work backwards’ to suggest that a vaccine wont work. They have had a Covid type vaccine for chickens for some years and of course far more infectious diseases like measles ( R=12!) are managed well by widespread vaccination.
3 years ago
For measles, we do have a vaccine that prevents asymptomatic infection and secondary transmission incredibly well. It’s still very unclear what the Covid vaccines do to transmission.
3 years ago
It may be also possible to learn about secondary transmission from within-household transmission rates for various combinations of vaccinated and unvaccinated people.
3 years ago
Kia ora Thomas, thank you for doing this writing, I enjoy and learn from every post. Keep it up.
3 years ago