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1. An hour ago I posted a thread explaining the concept of herd immunity and the problem of overshoot, whereby an epidemic infects more people that are required for herd immunity.
Despite disclaimers, people interpreted it as an endorsement of the herd immunity approach.
Despite disclaimers, people interpreted it as an endorsement of the herd immunity approach.
2. I think that it is important to talk about the science of epidemic models and how they work, so I am going to repost parts of the thread, but taking even more care to make it clear that allowing #COVID19 to go to herd immunity and beyond would be a disaster.
3. Given the uncertainties we face around the degree and duration of of acquired immunity, it is not even clear that one could reach herd immunity for #SARS2CoV.
But even if one could, the cost in lives would be unacceptable.
But even if one could, the cost in lives would be unacceptable.
4. The main point in the original thread was that if herd immunity requires 60% of the population to be infected, you can't just let the epidemic go unchecked and expect to suffer "only" 60% infected. This is because of something known as overshoot. Let's take a look.
5. Herd immunity—while a disastrous control strategy for this pandemic—is a key concept in epidemiological modeling. This is the state at which enough people are immune that a new outbreak cannot take off—because a new case infects fewer than one downstream cases.
6. In an SIR or SEIR model, herd immunity is reached when the effective reproductive number Re drops below one, where Re=R0 * S and S is the fraction of the population that is susceptible to infection. Herd immunity thus arises when the fraction susceptible drops below S=1/R0.
7. Assuming that immunity is complete and permanent—a huge assumption for #COVID19—herd immunity is reached once a fraction 1-1/R0 of the population has been infected. So if R0 is 2.5 for #SARSCoV2, herd immunity would require that 60% of the population become infected.
8. That's already untenably high.
But it's far worse. When an epidemic sweeps through, it won't stop once 1-1/R0 of the population have been infected.
This is because epidemics have momentum of a sort, and they overshoot the herd immunity threshold before coming to a halt.
But it's far worse. When an epidemic sweeps through, it won't stop once 1-1/R0 of the population have been infected.
This is because epidemics have momentum of a sort, and they overshoot the herd immunity threshold before coming to a halt.
9. (Reminder: hoping for herd immunity is a bad idea)
It turns out that in a basic SIR or SEIR model, the final size of an epidemic is not p=1-1/R0, but rather p=1-e^R0 p. @joelcmiller has a nice paper about this: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3506030/
It turns out that in a basic SIR or SEIR model, the final size of an epidemic is not p=1-1/R0, but rather p=1-e^R0 p. @joelcmiller has a nice paper about this: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3506030/
10. I can illustrate overshoot with a simple SEIR model of the COVID19 epidemic. These models have four types of individuals: susceptible, exposed, infectious, and recovered.
(Researches use more complex models for forecasting. But this model allows us to understand the effect.)
(Researches use more complex models for forecasting. But this model allows us to understand the effect.)
11. For those who want to see under the hood, here are the differential equations that describe this model. It is not necessary to understand these to understand what follows.
(Reminder: Herd immunity is not a viable control strategy for #COVID19)
(Reminder: Herd immunity is not a viable control strategy for #COVID19)
12. Let's see what these dynamics look like. Below I show the number exposed and infectious individuals over time, stacked atop one another, for parameters similar to those often used in #COVID19 models.
R0=2.5
Exposed period=average 3 days
Infectious period=average 8 days
R0=2.5
Exposed period=average 3 days
Infectious period=average 8 days
13. Now we visualize fractions of susceptible and recovered individuals as well. This is a stacked chart, so the shaded areas are proportional to the number in each category. Every "recovered" individual is a case. "Recovered" is a misnomer. Not all actually recovered. Some died.
14. If the epidemic stopped once we reached the herd immunity threshold, the turquoise curve would top out at the dashed line, with 60% of the population having been infected.
That would be bad enough. But it keeps going. Those extra infections are what we call "overshoot."
That would be bad enough. But it keeps going. Those extra infections are what we call "overshoot."
15. This overshoot represents a huge number of infections. For the model shown here, it represents nearly 30% of the population and nearly 33% of the total infections. So if letting the epidemic go through to herd immunity is even worse than it might sound.
16. Why is this happening? It takes place because an epidemic has something akin to momentum, in the form of people who are already infected when you reach the herd immunity threshold. An epidemic couldn't start anew from that place, but the current one can keep going.
17. In fact, for an SIR or SEIR model, you reach herd immunity not when the epidemic is nearly over, but rather *precisely* at the epidemic peak. This makes sense. Before the herd immunity threshold, each case creates >1 new cases, and the epidemic curve keeps increasing.
18. And that is the take-home point. Herd immunity without vaccination requires a huge number of infections, at least 1-1/R0. But in practice, you get far more people infected than that due to overshoot.
The cost in lives makes this approach untenable.
The cost in lives makes this approach untenable.
19. As a final note, overshoot is one of those important ideas that seemed to become common knowledge late in development of the field. I first learned about it in a paper by
@andreashandel: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2093965/
We also used it in our work here: https://academic.oup.com/emph/article/2014/1/150/1846924
@andreashandel: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2093965/
We also used it in our work here: https://academic.oup.com/emph/article/2014/1/150/1846924
