[ Question ]

Is there a theoretical upper limit on the R0 of Covid variants?

by CraigMichael1 min read26th Jul 20218 comments



Looking at the Wikipedia article on basic reproduction number, it looks like the most contagious virus (as of right now) is measles with an R0 (high estimate) of 18. I'm wondering if there is some asymptotic limit to how contagious viruses can get, and maybe measles is close there? If there is or isn't, do we have any ideas as to what biological mechanisms are related to this? 

I'm asking because it seems as the new variants emerge, it would be wise to aware of the worst case scenario. Just making a rough plot of the Covid rows in the basic reproduction article, and a rough stab on when they emerged, the wild-type, Alpha, Delta trend looks like this. 

Wild-type, Alpha and Delta R0s (upper limits) and approximate dates when they emerged

From Tomas Pueyo's excellent thread, it looks like as Covid gets more transmissible it's likely to get more deadly.

In 20 months Covid has went from an R0 (again, high estimate) of 3.4 to 8. I'm not an epidemiologist, but that seems like a really big jump in context. To be fair, again, I'm using the high estimates, but the general trend is concerning and I would sleep better knowing if there was some biological reason it would plateau.  

A scary, but I'm not sure how likely, scenario would be if another 20 months out (March 2023 or so), assuming there's large enough sections of the world where Covid is still spreading (either because vaccines haven't gotten there, or new vaccines are required for breakthroughs, or vaccines/infection immunity declines too quickly, etc), is there any reason to think it wouldn't jump another ~4.6 to ~12 or higher? Could it go above 18? 

 I'm just surprised I'm not seeing more discussion about this. Maybe I've missed it?

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I'm not bio-related or anything, but a popular theory is that what we're seeing in data (where different strains can be observed to develop mutations at a particular spot) can be explained by convergent evolution, which can possibly mean that the variants are running out of new adaptations and converging into local maxima.

Relevant scientific american article | Relevant bioRxiv preprint

Endorsed by someone who has been reading the literature obsessively.  The NTD can still get some mileage but most of the really interesting stuff has happened.

Perhaps too tongue in cheek, but there is a strong theoretical upper bound on R0 for humans as of ~2021. It's around 8 billion, the current world population.

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R is an variable that depends on the enviroment and is not a variable that the virus has independent of it's enviroment. 

My understanding is that's true for Rt (the effective reproduction rate) but R0 is a general "this is how contagious this virus is" measure. 

In reality, varying proportions of the population are immune to any given disease at any given time. To account for this, the effective reproduction number Re is used, usually written as Rt, or the average number of new infections caused by a single infected individual at time t in the partially susceptible population. 

I think you're correct that the difference between R0 and Rt is that Rt takes into account the proportion of the population already immune.

However, R0 is still dependent on its environment.  A completely naive (uninfected) population of hermits living in caves hundreds of miles distant from one another has an R0 of 0 for nearly anything. A completely naive population of immunocompromised packed-warehouse rave attendees would probably have an R0 of 100+ for measles.

I don't know if there is another Rte type variable that tries to define the infectiveness of a disease given both the prevalence of immunity and the environment. Seems like most folks just kinda assume that environment other than immune proportion is constant when comparing R0/Rt figures.

Dan, both you and Elizabeth make good points here that I hadn't given enough consideration to (I wish I could tag both of you in a comment somehow, but I'm not sure if that's possible). 

Yes, it is dependent on the population/community but also there's several different ways to calculate it making it hard to compare not just between diseases but also between R0 calculations for given diseases... So... yeah that makes a straight-forward objective ranking of contagiousness a much more difficult task I suspected from the table in the article... it also makes talking about contagiousness objectively somewhat more difficult than I hoped.

R0 is generally a pretty good "this is how contagious this virus is" metric, and is dependent on the environment. If two diseases have different R0s in the same environment, the one with the higher R is more contagious (modulo something really weird). But environmental changes can affect R0 as much as they affect Rt.