7 ms·

The tricky math of Covid-19 herd immunity

63 points by Anon84 6y ago

learnstats2 6y ago
I feel uninterested in R-nought (or R) when there is evidence for a huge variance around how many people each person will infect. Infections seem to happen at large gatherings: one person can be identified as infecting 50 others simultaneously, especially in the early cases, even though the R-nought is said to be no more than 2.5 That suggests infectiousness is an incredibly skewed distribution, to the point of implausibility. An epidemiologist apparently setting out R-nought as the underlying basis for their modelling (or even: communicating it to the public as such) worries me. I wouldn't begin any statistical modelling unless I was thinking about the distribution of infectiousness more generally: even a high school student of statistics would know to look beyond the mean and to the variance.
- mjevans 6y ago
  The statistics work the same way that aggregate physics work. Great at working with the whole, bad at the micro-level. Even after we drive the "R-nought" low enough that just means that on the whole the fire is 'contained' and will eventually burn out. To achieve actual eradication, which is what is required for something like this disease, a strong concerted effort to isolate and contain is required. I am also somewhat fearful that there will be a rush towards large events and other high-risk activities that allow these 1 to 50+ mega-exposures from prolific infecters to happen.
- PragmaticPulp 6y ago
  > An epidemiologist apparently setting out R-nought as the underlying basis for their modelling (or even: communicating it to the public as such) worries me. One of the core point of the linked article is that R0 has a wide range and therefore can’t be used to draw firm conclusions about herd immunity. > even a high school student of statistics would know to look beyond the mean and to the variance. I’m not sure if you’re responding to the linked article, but the article does a good job of emphasizing exactly that point. The R0 and her immunity calculations aren’t strict values or hard cutoffs. They are very situation dependent and will change over time depending on circumstances and behavior. It’s also important to keep in mind that the current average R0 numbers are measured during the middle of widespread social distancing and similar countermeasures. If people start reducing their precautions under the assumption that herd immunity will protect them, the infection rate might increase again.
- soneil 6y ago
  R:0 is an average, not a promise. It's that simple. Some people will infect 50 people at a wedding. Some people will spend a couple of weeks in bed having the time of their lives. Some people will just stop breathing. R is based on a populace, not a person.
- alimw 6y ago
  It remains a valuable descriptive statistic for the population as a whole. Your own model might do all sorts of clever stuff under the hood, but its prediction will be expressible to first order in terms of R₀ and that's what people are going to be interested in.
  - SpicyLemonZest 6y ago
    It's a valuable descriptive statistic, but it's very prone to misinterpretation. I've seen a lot of people follow sites like rt.live, where they claim to produce "up-to-date-values for R" and draw (their arbitrary estimate of) R=1 as the dividing line between good and bad. So I'm not sure it ends up as a net positive to the public's understanding of the virus.
- jacquesm 6y ago
  R0 is an observation, and an average at that. So of course there is huge variance, that's the whole reason we need it in the first place.
- jshen 6y ago
  You obviously didn’t read the article.
- dtech 6y ago
  Some people earn $0, others earn $1000000 a year. That doesn't mean mean an aggregate like mean income isn't useful
  - jessaustin 6y ago
    Income is a perfect example of a quantity for which mean is not an informative statistic. Really, anything more-or-less bounded on one side is not well-characterized by the mean.
  - learnstats2 6y ago
    It precisely does mean that mean income isn't useful. Governments don't (or shouldn't) quote it, because it tells you more about the richest person than it does about the population as an aggregate measure.
- newacct583 6y ago
  > I feel uninterested in R-nought (or R) when there is evidence for a huge variance around how many people each person will infect. Epidemics are by definition aggregate effects. They're defined by statistical models at all levels. Everyone involved understands that there is variance in individual cases. That's literally the whole point of the field inventing terms like R0! I genuinely don't understand what you're trying to say here. It sounds suspiciously like "I don't understand statistics so I refuse to believe in any models that use them."
  - learnstats2 6y ago
    What I'm trying to say is: I do understand statistics and therefore the mean is something I would not use in my modelling when there is a high skew in the data: here, the skew appears to be incredibly high - so the mean (here called "R0") is not reliable at all.
kayodelycaon 6y ago
Is this taking into account possible reinfection and mutation rates? There's a lot about the virus we don't know.
- zarathustreal 6y ago
  Exactly. Everyone’s talking about herd immunity without knowing if it’s A) possible or B) effective. When it mutates we’re back where we started
  - redisman 6y ago
    Wouldn’t that be the case with a vaccine too? Mutations could also move it away from the Goldilocks properties it has right now for massive spread.
- SpicyLemonZest 6y ago
  The controversies over reinfection were about the idea of immunity passports, which are much more sensitive to small errors - if 10% of people can get a mild reinfection, that's a rounding error in herd immunity but a distastrous gap in immunity passports. Epidemiologists are very confident that people who recover from the virus get substantial and reasonably long-lasting immunity.
  - fzeroracer 6y ago
    > Epidemiologists are very confident that people who recover from the virus get substantial and reasonably long-lasting immunity. Citation?
umvi 6y ago
Well, one thing's for sure - the USA will reach herd immunity more quickly than the rest of the world at the current rate. The thing that bugs me about covid-19 is how we only try to optimize for reducing deaths of that one thing (covid-19), while letting other types of collateral damage resulting from said optimizations pile up unaccounted for as side effects. Experts are clearly very bad at predicting second and third order side effects resulting from covid-19 death reduction optimization. To use a computer analogy, it's like going to extreme measures to refactor all programs so that Covid19Exception kills as few processes as possible, meanwhile processes left and right are dying at elevated rates due to HeartExceptions and BrainExceptions (and in a few months CancerExceptions) and the OOM Killer is on the prowl but nobody is noticing because they are hyperfocused on Covid19Exceptions.
- tomrod 6y ago
  The economic harm is generally recognized, and an EU type policy is seen as an better than most piecemeal implementations. Ironically, US consumer wages went up by adding $600 to US folks cashflow.[0] There are two big elephants in the room to consider: 1. Ongoing health effects from Covid. Hopefully not as bad, expensive, and detrimental as polio. 2. Chance for negative mutation. These two items alone add a lot of economic uncertainty. [0] https://www.vox.com/2020/5/29/21274416/household-income-surge-april-cares-act-coronavirus-stimulus https://www.vox.com/2020/5/29/21274416/household-income-surg...
- svaha1728 6y ago
  First we assumed that since it was a coronavirus the summer wouldn't be a problem. Now we assume that if we just hurry up and infect everyone we can reach herd immunity. That is another assumption, it isn't yet clear if infection with the COVID-19 virus makes a person immune to future infection. It might be true, but the most certain among us don’t seem to be the smartest.
  - umvi 6y ago
    > Now we assume that if we just hurry up and infect everyone we can reach herd immunity. Well, how long will it take to reach 60% with/without heavy preventative measures? If SIP/masks/social distancing drag out the timeline so it takes 5 years to reach herd immunity... you'll have a mental health crisis of the millennium to deal with in addition to covid-19.

63 points by Anon84 6y ago

I feel uninterested in R-nought (or R) when there is evidence for a huge variance around how many people each person will infect. Infections seem to happen at large gatherings: one person can be identified as infecting 50 others simultaneously, especially in the early cases, even though the R-nought is said to be no more than 2.5 That suggests infectiousness is an incredibly skewed distribution, to the point of implausibility. An epidemiologist apparently setting out R-nought as the underlying basis for their modelling (or even: communicating it to the public as such) worries me. I wouldn't begin any statistical modelling unless I was thinking about the distribution of infectiousness more generally: even a high school student of statistics would know to look beyond the mean and to the variance.

mjevans 6y ago
The statistics work the same way that aggregate physics work. Great at working with the whole, bad at the micro-level. Even after we drive the "R-nought" low enough that just means that on the whole the fire is 'contained' and will eventually burn out. To achieve actual eradication, which is what is required for something like this disease, a strong concerted effort to isolate and contain is required. I am also somewhat fearful that there will be a rush towards large events and other high-risk activities that allow these 1 to 50+ mega-exposures from prolific infecters to happen.
PragmaticPulp 6y ago
> An epidemiologist apparently setting out R-nought as the underlying basis for their modelling (or even: communicating it to the public as such) worries me. One of the core point of the linked article is that R0 has a wide range and therefore can’t be used to draw firm conclusions about herd immunity. > even a high school student of statistics would know to look beyond the mean and to the variance. I’m not sure if you’re responding to the linked article, but the article does a good job of emphasizing exactly that point. The R0 and her immunity calculations aren’t strict values or hard cutoffs. They are very situation dependent and will change over time depending on circumstances and behavior. It’s also important to keep in mind that the current average R0 numbers are measured during the middle of widespread social distancing and similar countermeasures. If people start reducing their precautions under the assumption that herd immunity will protect them, the infection rate might increase again.
soneil 6y ago
R:0 is an average, not a promise. It's that simple. Some people will infect 50 people at a wedding. Some people will spend a couple of weeks in bed having the time of their lives. Some people will just stop breathing. R is based on a populace, not a person.
alimw 6y ago
It remains a valuable descriptive statistic for the population as a whole. Your own model might do all sorts of clever stuff under the hood, but its prediction will be expressible to first order in terms of R₀ and that's what people are going to be interested in.
- SpicyLemonZest 6y ago
  It's a valuable descriptive statistic, but it's very prone to misinterpretation. I've seen a lot of people follow sites like rt.live, where they claim to produce "up-to-date-values for R" and draw (their arbitrary estimate of) R=1 as the dividing line between good and bad. So I'm not sure it ends up as a net positive to the public's understanding of the virus.
jacquesm 6y ago
R0 is an observation, and an average at that. So of course there is huge variance, that's the whole reason we need it in the first place.
jshen 6y ago
You obviously didn’t read the article.
dtech 6y ago
Some people earn $0, others earn $1000000 a year. That doesn't mean mean an aggregate like mean income isn't useful
- jessaustin 6y ago
  Income is a perfect example of a quantity for which mean is not an informative statistic. Really, anything more-or-less bounded on one side is not well-characterized by the mean.
- learnstats2 6y ago
  It precisely does mean that mean income isn't useful. Governments don't (or shouldn't) quote it, because it tells you more about the richest person than it does about the population as an aggregate measure.
newacct583 6y ago
> I feel uninterested in R-nought (or R) when there is evidence for a huge variance around how many people each person will infect. Epidemics are by definition aggregate effects. They're defined by statistical models at all levels. Everyone involved understands that there is variance in individual cases. That's literally the whole point of the field inventing terms like R0! I genuinely don't understand what you're trying to say here. It sounds suspiciously like "I don't understand statistics so I refuse to believe in any models that use them."
- learnstats2 6y ago
  What I'm trying to say is: I do understand statistics and therefore the mean is something I would not use in my modelling when there is a high skew in the data: here, the skew appears to be incredibly high - so the mean (here called "R0") is not reliable at all.

kayodelycaon 6y ago

Is this taking into account possible reinfection and mutation rates? There's a lot about the virus we don't know.

zarathustreal 6y ago
Exactly. Everyone’s talking about herd immunity without knowing if it’s A) possible or B) effective. When it mutates we’re back where we started
- redisman 6y ago
  Wouldn’t that be the case with a vaccine too? Mutations could also move it away from the Goldilocks properties it has right now for massive spread.
SpicyLemonZest 6y ago
The controversies over reinfection were about the idea of immunity passports, which are much more sensitive to small errors - if 10% of people can get a mild reinfection, that's a rounding error in herd immunity but a distastrous gap in immunity passports. Epidemiologists are very confident that people who recover from the virus get substantial and reasonably long-lasting immunity.
- fzeroracer 6y ago
  > Epidemiologists are very confident that people who recover from the virus get substantial and reasonably long-lasting immunity. Citation?

umvi 6y ago

Well, one thing's for sure - the USA will reach herd immunity more quickly than the rest of the world at the current rate. The thing that bugs me about covid-19 is how we only try to optimize for reducing deaths of that one thing (covid-19), while letting other types of collateral damage resulting from said optimizations pile up unaccounted for as side effects. Experts are clearly very bad at predicting second and third order side effects resulting from covid-19 death reduction optimization. To use a computer analogy, it's like going to extreme measures to refactor all programs so that Covid19Exception kills as few processes as possible, meanwhile processes left and right are dying at elevated rates due to HeartExceptions and BrainExceptions (and in a few months CancerExceptions) and the OOM Killer is on the prowl but nobody is noticing because they are hyperfocused on Covid19Exceptions.

tomrod 6y ago
The economic harm is generally recognized, and an EU type policy is seen as an better than most piecemeal implementations. Ironically, US consumer wages went up by adding $600 to US folks cashflow.[0] There are two big elephants in the room to consider: 1. Ongoing health effects from Covid. Hopefully not as bad, expensive, and detrimental as polio. 2. Chance for negative mutation. These two items alone add a lot of economic uncertainty. [0] https://www.vox.com/2020/5/29/21274416/household-income-surge-april-cares-act-coronavirus-stimulus https://www.vox.com/2020/5/29/21274416/household-income-surg...
svaha1728 6y ago
First we assumed that since it was a coronavirus the summer wouldn't be a problem. Now we assume that if we just hurry up and infect everyone we can reach herd immunity. That is another assumption, it isn't yet clear if infection with the COVID-19 virus makes a person immune to future infection. It might be true, but the most certain among us don’t seem to be the smartest.
- umvi 6y ago
  > Now we assume that if we just hurry up and infect everyone we can reach herd immunity. Well, how long will it take to reach 60% with/without heavy preventative measures? If SIP/masks/social distancing drag out the timeline so it takes 5 years to reach herd immunity... you'll have a mental health crisis of the millennium to deal with in addition to covid-19.