I'm seeing a lot of discussions on the question on whether it's worse to have a pathogen that's x% more lethal or one that's x% more transmissible (with respect to some baseline). The only valid answer here is: IT DEPENDS ON MANY THINGS. 🧵⤵️ •1/15
One argument that definitely DOES NOT hold is “x% more transmissible will overgrow x% more lethal because the former is a factor inside the exponential while the latter is outside and the exponential will dominate it” which I see a lot. •2/15
Yes, it IS true mathematically that C₁·exp(c₁·t) will overgrow C₂·exp(c₂·t) (for t→+∞) when c₁>c₂ no matter what C₁,C₂>0 are, but… in a finite population, exponential growth has to stop at some point! •3/15
And yes, I've seen this kind of argument a number of times. For example: 🔽
https://twitter.com/gro_tsen/status/1470429622412136451(scroll up to see more context). •4/15
It's amazing how often people talk about exponential growth and conveniently “forget” to say anything about the end of that exponential growth. So remember: “exponential growth” alone says NOTHING about the final number of infected (attack rate). •5/15
The problem is that nobody knows how to predict how and when exponential growth stops. We have trivial epidemiological models like SIR, but they are very far from reality (e.g., they predict a single wave which, as you may have noticed 😐, didn't quite work out). •6/15
But still, we might ask the SIR model, if only as a starting point, what it thinks about “x% more transmissible” vs “x% more lethal”, and its answer is very much “IT DEPENDS”. See thread below 🔽 for some example graphs:
https://twitter.com/gro_tsen/status/1345343184642179074•7/15
This isn't really surprising when you think of it: if you have a pathogen with R₀ equal to 1 000 000, well, EVERYONE is going to be infected. If it's twice or 1000× that — the same. So ONLY the lethality rate matters. •8/15
It's unclear whether we're in this territory with covid, but the fact with plain SIR is that the final attack rate of unmitigated epidemic is very soon close to 100%, so R₀ changes the rate at which it happens, not so much the attack rate in question. •9/15
As an aside, it's funny how many people have tried to scare us with super-duper-high (and honestly meaningless) R₀ values for α and δ variants which put us well in the “well, essentially everyone will be infected anyway” territory, now needing to backtrack! •10/15
Because if everyone will be infected with δ and everyone will be infected with ο, well, clearly, lethality is the thing we care most about. So by exaggerating the importance of infectiousness, these people have shot their own arguments in the foot. •11/15
Now one might say, well, the dynamics matter immensely: even if everyone will get infected, the speed at which they do matters, because it affects whether the health system will get overrun. Indeed! This is crucial: lethality is not fixed at all. •12/15
But even taking this into account the case isn't clear-cut: on the one hand you have x% more people needing to go to the hospital (wrt baseline), on the other hand you have the same number but at a rate x% higher. So the peak rates should still be comparable. •13/15
And of course, in real life, all of this is made tremendously more complicated by the presence of vaccines with only partial effectiveness. I would like to remind that there are some hidden variables here: see 🔽⏬
https://twitter.com/gro_tsen/status/1456197184790142980•14/15
So, no, there's no simple answer. Or rather, the only valid answer is “we don't know: it depends on many factors”. And even if we did know, what would be the point? it's not like we're offered a choice between Scylla and Charybdis anyway! we don't get to pick our virus. •15/15
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