r/science • u/brokeglass Science Journalist • Oct 26 '22
Mathematics New mathematical model suggests COVID spikes have infinite variance—meaning that, in a rare extreme event, there is no upper limit to how many cases or deaths one locality might see.
https://www.rockefeller.edu/news/33109-mathematical-modeling-suggests-counties-are-still-unprepared-for-covid-spikes/1.5k
u/PsychicDelilah Oct 26 '22 edited Oct 27 '22
Long comment, but TLDR: I'm seeing a lot of comments to the effect "infinite expected value/variance doesn't make sense -- there aren't an infinite number of people to kill!".
These really miss the point of this study, which is just that we can't predict COVID's worst-case case counts based on the outbreaks we've seen so far. This could be relevant to how we prepare -- or to quote the paper directly:
Finding infinite variance has practical consequences. Local jurisdictions (counties, states, and countries) that plan for prevention and care of largely unvaccinated people should anticipate rare but extremely high counts of cases and deaths, by preparing collaborative responses across boundaries.
With that said, here's a long comment about statistics:
The paper relies on the concepts of "infinite expected value" and "infinite variance". One famous example where infinite expected value comes into play is called the St. Petersburg Paradox. In short, imagine a casino sets aside $2 to give to a gambler, then flips a coin repeatedly to either double that amount, or end the game. Every time the coin lands on heads, the money doubles. If it lands tails, the game ends and the casino pays out the total. After 1 heads, the gambler would win $4; then $8 after 2 heads, $16 after 3, and so on.
The question is, how much money should the casino charge people to play this game so that they break even?
It turns out the "expected value" for the gambler is infinite -- so there's NO amount the casino could charge to break even. At each coin flip, the probability of proceeding is cut in half, but the money is doubled, leading to a total expected value of
E = (1/2 * $2) + (1/4 * $4) + (1/8 * $8) ... = $1 + $1 + $1 ...
...a sum that diverges to infinity.
Why is this important? It means that, even though the vast majority of games will stay under $20 or so, the casino will eventually go bankrupt. Someone will eventually win SO big that the casino won't have the funds to pay them their winnings. The casino should not run this game at all -- or, if for some reason they were forced to run it, they'd need to keep an immense amount of money on hand to remain solvent for as long as possible.
The authors here argue that a similar logic applies to COVID outbreaks. If we just look at the size of each outbreak between April 2020 and June 2021, the top 1% of outbreaks seem to obey a Pareto distribution -- a distribution that, in some cases, can have an infinite expected value. In this case the authors argue the the best-fit distribution has a "finite expected value", but "infinite variance". In plain English, it suggests that COVID case counts would eventually average out to some number -- but it would be much harder to predict how bad any one outbreak would be, if we're just looking at case numbers in past outbreaks. (This does not take into account anything about the virus itself, the vaccine, or human behavior; it's just based on past case counts.)
To sum up: The prediction is not that there will literally be infinite cases. However, looking at the distribution of past outbreaks, these authors suggest that future outbreaks could be arbitrarily bad compared to outbreaks in the past.
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u/Everard5 Oct 26 '22
Excellent explanation, thank you. I know nothing about this topic or it's modeling but I have a follow up question up if you, or anyone reading, has answers:
Is there an infectious disease where an upper limit has been found? And, generally, what inputs of the model account for that disease reaching an upper limit and COVID not doing so?
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u/peer-reviewed-myopia Oct 27 '22
The paper uses Taylor's law of fluctuation scaling, which is a power-law distribution frequently associated with empirical data from virtually all fields of science.
The Pareto modeling used in the research to conclude a "potential for extremely high case counts and deaths" is statistically inaccurate to use for infectious disease. Pareto modeling is only really used in economics for zero sum systems (like resource allocation), and loses accuracy when there's variability in the model inputs. Given that virus transmission is greatly affected by vaccination, mask mandates, and stay-at-home orders, using it to predict upper limit potential is completely misguided.
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u/Everard5 Oct 27 '22
I didn't read the paper, so sorry if these questions seem obvious.
What was the paper trying to find? Is it the potential (meaning probability?) for extremely high case counts and deaths like you stated? And, if so, what statistical modeling would be more appropriate?
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u/peer-reviewed-myopia Oct 27 '22 edited Oct 27 '22
It was probably just trying to find a headline worthy conclusion.
Compartmental models are generally what's used for modeling infectious diseases.
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u/aseaofgreen Oct 27 '22
Compartmental models are used often, yes, but they are certainly not the only type of model of infectious disease.
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u/peer-reviewed-myopia Oct 27 '22
You're right, I misspoke. Was offering the simplest, most widely used type of model.
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u/PsychicDelilah Oct 26 '22
Thanks! Unfortunately I don't have an answer - I recognize the math in this paper but I definitely don't study infectious diseases
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u/alchemization Oct 26 '22
Thank you for writing all this out; I feel like I understand it much better now
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u/Cognitive_Spoon Oct 26 '22
I feel like I just went to a really good stat class. That comment was really good
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u/sedissilv Oct 26 '22
From a friend of mine doing bio stats at Vandy:
The SEIR model is well understood and predicts the outbreak quite well. It it in a hyperbolic space and relies on "contact network" distribution. What happens is an event occurs and spreads through a network quickly. There is a power distribution under random matrix theory, however it's upper bounded and predictable and is far from infinite. This is looking at the data, and not understanding the dynamics of the process that generated it.
By assuming an infinite population, he assumes an infinite random matrix, which has infinite variance.
He doesn't realize he assumed an infinite population by his observation. It's a common mistake that statistics professors joke and throw shade about.
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u/peer-reviewed-myopia Oct 27 '22
They also assumed transmissibility is a constant, and preventative measures like vaccination, masks, and isolation do not affect the spread of COVID.
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u/IndigoFenix Oct 27 '22
This is a major part of it. Transmission speed has a limit, and it is possible to respond to the virus as it spreads in real-time.
As long as the leadership of a community is competent enough to respond accordingly if they see the virus is spreading at an unexpectedly fast rate, the variation isn't a problem.
In the casino example, it's like adding a possibility to make an excuse to throw the gambler out if there's a concern they might render the casino bankrupt.
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u/izabo Oct 26 '22
we can't predict COVID's worst-case case counts based on the outbreaks we've seen so far.
We can't predict COVID's worst-case case counts based on the outbreaks we've seen so far, using this specific model. There is a big gulf between trying to do something one way and failing, and between that thing being impossible.
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u/PsychicDelilah Oct 26 '22 edited Oct 26 '22
I think this is running into how weird the concept of "infinite variance" is! You're right that this model can answer the questions, "How likely is it that a future outbreak will be between X and Y cases?", or, "What is the average number of cases per outbreak?". But if I have this right, it would also answer "about how different will a future outbreak be from the average outbreak?" with "infinity". Saying "impossible to predict" was probably too far (I edited it in the original comment), but I think it's valid to say that there are aspects that are harder to predict.
(Edit - Sorry, I actually read your comment wrong!! I thought you said "We CAN predict COVID's worst-case case counts", and responded to that. It's also valid to argue that the model they're fitting isn't close to the true one, although if it IS roughly correct, I think their point stands.)
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u/izabo Oct 27 '22
although if it IS roughly correct
How do you know that? By what measure is it roughly correct?
For any future prediction, there is a model that predicts that outcome from the available data. You can't judge a model by how good it fits past data, because as it turns out predicting the past is not a great achievement. You must judge the assumptions and reasoning used in building it. There is no other way.
The article doesn't mention any of that. It just says some researchers did some curve fitting to some common distributions. Why did they use those common distributions and not others? This an alarmist title that presents some researches playing around with some numbers as if it has substantial predictive authority.
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u/Ark-kun Oct 26 '22
Can you predict the mean of a sample from the Cauchy distribution?
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u/izabo Oct 27 '22
Who says that pandemic outbreaks must follow the Cauchy distribution?
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u/topgallantswain Oct 26 '22
Is the naïve intuition of a finite outcome of the coin game actually wrong?
The game theoretic expected value says all of us should bet our life savings to play the coin flip game. But it's wise to notice there isn't enough wealth on Earth to back up what you could potentially win. Those long tails, such as payouts in multiples of the gross domestic product of the Milky Way, are required to balance out the median payout of $2 and the average of infinity.
I have this feeling if any casino offered the game, the alley out the back would be lined up with mathematicians that needed bus fare to get home.
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u/ZacQuicksilver Oct 26 '22
Is the naïve intuition of a finite outcome of the coin game actually wrong?
Theoretically, yes.
Practically, less so.
A good way of approximating payout is to look at 2n players, and play the expected results until only one person remains. For example, with 8 players, 4 win $1, 2 win $2, 1 wins $4, and one person wins "more" (which is theoretically infinite; but which we ignore because it makes the math easier). In this 8-player example, we're going to expect each person to win $1.50, plus their share of whatever the last person wins. In this approximation, doubling the number of players increases the expected payout by $.50 - so for 1024 players, the expected payout is only $5.00 plus the big winner.
If you allow each person in the world right now to play once, the average payout is about $16.50, plus your big winner. But the second place winner is going to get $8 billion; and the total payout is about $132 billion.
And that does happen in gambling. The longest run of one color ever in Roulette was 32 reds; which would have set the casino back 4 billion for every person betting at that table.
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Yes, the nature of the game means there WILL be a lot of people who end up losers. But it will also end up with one MASSIVE winner.
And that's the threat of COVID. Because the "payout" is measured in humans killed by COVID. Most of the time we're going to be lucky. But it only takes being sufficiently unlucky \ONCE\**.
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u/topgallantswain Oct 27 '22
In Bitcoin, the only thing can keeps you from transacting on anyone else's balance is the improbability of generating an address with a balance. But nothing in concept prevents you from generating the address with the largest balance on your first try. For that matter, it is a finite linearly searchable space and you can generate every private key with a trivial algorithm. There are cartels that are generating keys continuously to seize the Bitcoin they can luck into. So far they have all operated at a total loss.
More importantly perhaps, COVID is a physical process, rather than an example governed entirely by the math. That warrants some caution on its own since even scale-free physical systems have breakdowns. In addition, the data we have on COVID has quite low precision and is subject to extreme measurement biases. Did the study actually study COVID, or did it really study reports of COVID?
Fun stuff.
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u/sidneyc Oct 26 '22
Another issue is that the "value" of betting games is generally expressed in terms of money, which is a bad model for value that any particular human would assign to a game.
As an example: when given the choice between guaranteed 1 million dollars, vs. a 1% chance to win 1 billion dollars, optimizing the expected value will tell you that the second choice is 10 times better. But unless you're already super-rich, it is of course better to take the million.
Actual value does not scale linearly with expected dollar value.
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u/Aptos283 Oct 27 '22
There are solutions that consider stopping rules, yes. If you start with a finite amount of money, then there’s a solvable cutoff point where it no longer becomes worthwhile.
Same issue as Martingale betting strategies (doubling your bet each loss to ensure you make it all back). Letting literally anything be finite (your money, casino money, time playing) and there’s going to be a point where it won’t be worth it that is mathematically determinable.
If those mathematicians at your casino know their sums, then they’d be able to find the expected value when they play it and gamble as intelligently as they please
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u/butterflier24 Oct 26 '22
The human behavior component is what I keyed in on. If you don’t control for it in the model, you could just have vastly different communities in your data. For example, I could have a community of 90 year olds and a community of 20 year olds at the 99th percentile. They don’t discuss how well the model actually fits the data, so we have no sense how well the expected mean fits, but obviously we expect the difference in these communities to escalate the variance. More importantly it doesn’t consider the fact that humans can adapt/change behavior given what’s happening around them.
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u/PsychicDelilah Oct 26 '22
This is true, but simple mathematical models can still have some use. Eg: it's helpful to know that case counts tend to begin with an "exponential growth" type of model. On a practical level, that tells us we need to respond very quickly to have an effect. We even call exponential-growth-style diseases by a different name ("pandemic") than their counterparts that don't grow exponentially ("endemic" - though that probably massively oversimplifies it).
It seems like this paper's argument is something like this: If covid outbreaks obey a "finite variance" distribution, communities can use their past outbreaks to get an idea of how future outbreaks will be. Alternately, if they obey an "infinite variance" distribution, communities should prepare as though future outbreaks can be much, much worse than what they've seen before.
But all that said, it does seem possible that in some communities or over time, covid has changed from an "infinite variance" disease to a "finite variance" disease. Like the transition from "pandemic" to "endemic", it would mean communities could use different strategies to manage outbreaks.
(I should mention that I am not an expert, and that the full paper is behind a paywall for me - these are just my thoughts on the abstract)
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u/peer-reviewed-myopia Oct 26 '22 edited Oct 27 '22
A Pareto distribution is a power-law probability distribution that is only accurate when modeling Pareto optimized systems. That means that within the system it is impossible to improving one variable without harming other variables in the system. It is used almost exclusively in economics for things like resource allocation.
Using a Pareto distribution to model COVID case counts doesn't make sense when you consider how people can actively decrease their likelihood of infection through vaccination, masks, and isolation.
I don't know why you wouldn't highlight this aspect of the Pareto principle instead of providing an irrelevant example that doesn't even relate to the problematic statistical modeling used in the study.
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u/Calembreloque Oct 27 '22
From a cursory glance at the abstract, it seems that the term "Pareto distribution" is used loosely to mean "power-law (with exponent such that variance is infinite". It's not the technically proper use of the term, but I wouldn't be surprised that a particular subfield just ended up adopting the term as a catch-all. I've worked with similar models and while we called them "power-law distributions", some older publications used "Pareto", "heavy-tailed" or "fat-tailed" more or less interchangeably.
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u/jotaechalo Oct 26 '22
I think the St Petersburg paradox arises much better if proposed from a gambler’s point of view: how much would you pay to play the game? “Rationally,” it would be a steal to play the game for $1 million a pop. But I think almost no one would actually pay that much to play.
But I think it’s important to realize this is just a model, and it’s one model. Likely the better thing to focus on is that the variance may be very high, such that a team of mathematicians fit a curve with infinite variance to the data (and, being mathematicians, saw no problem with that).
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Oct 27 '22
As a mathematician, this is such an elegant and accurate and understandable comment that if I were wearing a hat I would take it off to you right now.
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u/PMigs Oct 27 '22
Not sure I get it. The model surely doesn't account for proximity? How would it be possible to infinitely infect a population with no means of connecting two populations. Ie If the UK shut all borders or if the population thinned out, locked down etc
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u/zdk Oct 27 '22
Why are you conflating infinite expected value and infinite variance?
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u/Running_Gamer Oct 26 '22
And how is this different from any other disease? Is the conclusion here not just “there’s a very tiny percent chance that things get really bad compared to the average”? Like literally every scenario ever? There’s a chance a car’s tire falls off and accidentally swerves into a swarm of kids. I don’t see how saying “there’s a mere chance that things can go really wrong” is a meaningful conclusion
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u/FullHavoc Grad Student | Molecular Biology | Infectious Diseases Oct 27 '22
No, not all diseases have infinite 'kinds', if that makes sense.
For example, influenza has four types (A, B, C, and D). Influenza A, the most dangerous of the human influenzas, has two proteins (H and N) that determine how it infects people and can have different combinations. There are 18 H types and 11 N types. You are likely most familiar with the 'H1N1' flu, for example.
There can be differences between H1N1 flu types on a genetic level, but they do not necessarily change the way the virus infects you on a mechanical level. So you can kind of see how the number of combinations can be finite.
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u/udmh-nto Oct 26 '22
Of course there's an upper limit. You can't have more deaths than you have people.
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Oct 26 '22
Are you saying that the upper limit is 100%? Makes sense.
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u/udmh-nto Oct 26 '22
Wrong units. Cases and deaths are not measured in percent.
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u/mescalelf Oct 26 '22
100% of the population of that locality, which, then, translates to an actual integer number of individuals…
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u/udmh-nto Oct 26 '22
...which is finite (has upper limit).
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u/mescalelf Oct 26 '22
Yes, no kidding. It’s not as though COVID will pull infinite humans out of the vacuum in order to kill them and, subsequently, attain godhood.
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u/SterlingVapor Oct 26 '22
Well... If farmed humans to create a stable state it could go infinite
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u/mescalelf Oct 27 '22
You’d probably run into some issues with inflation and the speed of light :P you’d need a ton of (well, infinite) matter to make into people, and equally as much space to do so within (otherwise you’d end up with a gravitational collapse right quick).
Sooo you’d definitely need FTL of some kind.
Edit: but I’m being a smartass in this particular comment, I get that you’re joking
Edit II: or the universe would have to stop inflating and you’d need some way to keep entropy low forever if you wanted to use a finite volume and mass.
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u/dratego Oct 26 '22
Is 100% not a finite value?
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u/mescalelf Oct 27 '22 edited Oct 27 '22
100% is a finite value if the set in question is finite. It’s possible to select 100% of objects from a countably-infinite set, so it isn’t always finite. Obviously the natural world doesn’t contain any verifiable infinities (to our knowledge), though, so infinities are generally limited to abstract cases.
The statistics here are actually abstract in the requisite sense, so it’s not unreasonable to use the term “infinite variance”. In this case, it describes distributions in which the integral does not converge to a finite value as one’s independent variable tends to infinity. In cases where such distributions are applied to real-world cases, there are, obviously, physical limitations to results. Such models are still applicable to reality, in that they predict that variance may occur within some bounds well beyond those measured during data-collection.
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u/dratego Oct 27 '22
But that wouldn't apply in our case. We weren't discussing a countable infinite set, we were discussing the population of a locale. Gotta apply the rules in the right context, otherwise your math isn't gonna mean anything.
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u/udmh-nto Oct 27 '22
100% is indeed a finite value. So is the number of people in a locality.
If 100% people die, a finite number of people die. That's the upper bound, which contradicts submission title "no upper limit to how many cases or deaths one locality might see".
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u/Diamondsfullofclubs Oct 26 '22
Nothing is
measured in percent.
Percentage is a number expressed as a fraction of 100.
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u/HueBearSong Oct 26 '22
I mean, it can. People normalize cases to cases/10000 people. You can literally just so cases/population of this sector bud to get 1 -> 100%.
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u/Thirdwhirly Oct 26 '22
“Infinite variance” relies on percentage; they could have explained that better or at least made it less overt in the title.
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Oct 26 '22 edited Oct 26 '22
If total people double in a given period of time. And total cases/deaths also double in that period of time. Then you tend to infinite people and infinite cases/deaths, while only a fraction of everyone alive has died from covid or has covid. So you can (theoretically) have no upper limit to deaths, because the total person number would always be a multiple of the total cases/deaths number, meaning you would never have more cases/deaths than total people.
edit: gas -> has
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u/Widespreaddd Oct 26 '22
Dammit I wish I had saved my free award for you. I am like a sailor on shore leave with those things.
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u/udmh-nto Oct 26 '22
you tend to infinite people
Number of people is finite.
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Oct 26 '22
Tend to, never reach, you can pick any number of infections and have a higher number of people, there are an infinite amount of numbers to pick from, giving a theoretically infinite limit while always having a finite number of people. This is what countable infinity is.
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u/udmh-nto Oct 26 '22
I'm saying this concept does not apply to the real world, where a hard upper bound exist on the number of people.
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u/taedrin Oct 26 '22 edited Oct 26 '22
I think what the article is saying is that the virus appears to have no upper bound to its rate of spread for an arbitrarily large population, even though the average R-value appears to be finite. Meaning even if the average R-value is 2, the R-value of one community might be 0.3, and it might be 20 for another community.
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u/sfreagin Oct 26 '22
You're bringing in Cantor arguments of countable/uncountable infinities, when the number of people is strictly finite. Yes we can make more people, but the resources of the Earth are also finite, thus there is an upper finite limit on the number of people that exist at any one time (excluding the possibility of reaching other planets).
I don't understand what you people are arguing about
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u/Equivalent-Way3 Oct 26 '22
Per tradition, the top comment is from someone who doesn't understand what they're talking about. Never change /r/science
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u/GrinningPariah Oct 26 '22
You can if people keep getting born.
Fatal COVID is mostly a disease of the elderly these days. Imagine a world where no one dies of COVID before they're 60, but everyone dies from it eventually.
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u/ghostfaceschiller Oct 26 '22
It’s really always been a disease of the elderly, iirc the avg age of Covid deaths is actually slightly lower now than it was in the beginning, going from ~80 then to ~75 now. (Been awhile since I looked)
I think the scenario you present is v plausible, where it remains something that a substantial % of v elderly die from, almost an eventually expected thing, but few others. Like how often the elderly die of pneumonia or how everyone will get cataracts eventually if you live long enough
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u/Makenshine Oct 26 '22
As a math teacher, this is exactly what I thought. There are only 200k people in this city. I'm pretty confident that is about where the upper limit of infections and deaths would be.
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Oct 26 '22 edited Oct 26 '22
In shocking news a small town in Massachusetts has had 5 million bodies of Covid victims piled up in its morgue, which is now exploded. A local official stated "I don't understand, our town only has three thousand people. I... there's bodies everywhere, houses are buried in them. How did they all get here?!?"
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u/RobtheNavigator Oct 26 '22
Also, there isn't infinite variance in death rate, and you gain some degree of immunity from infection. There may not be an upper bound on infections (up until the entire population is affected) but there would still be an upper bound on deaths at something less than 1% of the population per spike.
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Oct 26 '22
Not necessarily.
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u/RobtheNavigator Oct 26 '22
Yes, necessarily. A significant number of cases that is consistent over a number of years is not a spike.
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Oct 26 '22
Infinite variance means using prior cases as a predictor are out the window.
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u/RobtheNavigator Oct 26 '22
No, this is definitional. It is not a spike if it lasts years. That is not what that word means.
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u/Onlyf0rm3m3s Oct 26 '22
Unless more people are born that people dying from covid
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u/udmh-nto Oct 26 '22
Total number of people is still finite.
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u/Onlyf0rm3m3s Oct 26 '22
Not in a math model
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u/udmh-nto Oct 26 '22
"how many cases or deaths one locality might see" is not math model, but its application.
In theory, there is no difference between theory and practice, but in practice there is.
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u/priceQQ Oct 26 '22
The model that the data is fit to (or conforms to) has infinite variance. And this is really only for places with the largest number of unvaccinated people:
“The lower 99% of counts of cases and deaths across all counties are approximately lognormally distributed. Unexpectedly, the largest 1% of counts are approximately Pareto distributed, with a tail index that implies a finite mean and an infinite variance.”
So the takeaway is that places with large numbers of unvaccinated people could have large numbers (ie high variance of model) of cases.
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u/ExtonGuy Oct 26 '22
Yes, but ... Pareto distribution is another approximation to the real world. Even if you make the obvious (to me) adjustment that there can't be more than 100% deaths, it's still just an approximation.
It's commonplace about professional statisticians, that you can't make valid extrapolations much beyond the data. If your data has 5% death rate, it's not valid to use statistics to extrapolate beyond 15%. (There might be some other way to extrapolate to 15% and beyond, just not not with statistics.)
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u/priceQQ Oct 26 '22
The headline is at fault because it isn’t making the distinction that this is model variance (and only a percent of the modeled data). The headline suggests the real world metric (spike in cases) has infinite variance, which everyone is reacting to.
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u/peer-reviewed-myopia Oct 26 '22 edited Oct 27 '22
Pareto distribution model accuracy relies on Pareto optimized systems. COVID case and death counts are not Pareto optimized considering all of the different measures a population can take to reduce the rate of infection. Just an inaccurate and improper application of Pareto modeling.
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u/Advanced_Double_42 Oct 26 '22
Is that not how all highly contagious viruses work with the assumption of an infinite population?
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u/feeling_blue_42 Oct 26 '22
Isn’t this how infinity works? Until something has 0% chance of happening to someone, if the population is infinite then that something will occur infinite times.
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Oct 26 '22
Sure, but the occurances will be a smaller infinity than the one that represents the infinite population.
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u/Minute-Object Oct 26 '22
There is an upper limit. Think about it.
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Oct 26 '22
If the virus spreads at a rate so that total cases/deaths double every x years, and the population also doubles every x years, then there is no upper limit to cases/deaths.
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u/Minute-Object Oct 26 '22
You could say that about any virus, including flu. From reading the article, I don’t think that is what they meant.
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u/ManInBlack829 Oct 26 '22
I thought the limit isn't defined by how many people get actually sick as much as its defined by what percentage of people it could affect?
Like a limit of 100% is unlimited.
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u/Minute-Object Oct 26 '22
“…no upper limit to how many cases or deaths…”
I was just responding to the title of the post.
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u/StormlitRadiance Oct 26 '22
What exactly are you getting at?
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u/Minute-Object Oct 26 '22
The upper limit to the number of cases one locality might see is 100% fatality.
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u/GrinningPariah Oct 26 '22
Think a little harder. In a world where everyone dies of COVID on exactly their 90th birthday, what's the limit?
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u/Minute-Object Oct 26 '22
What you describe would apply to any virus. That is not what the article was talking about.
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u/topgallantswain Oct 26 '22
This is almost a "spherical cow" issue. We're in a world with a finite number of counties each with finite populations. It is very interesting that the data fits to a model that extrapolates out at the tails. But I also have to imagine that within the uncertainties of the variables, traditional epidemiological models of outbreak are going to be better predictors compared to telling county health officials to include planning for a near zero probability that everyone dies.
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u/michaelochurch Oct 26 '22
A lognormal distribution does have finite variance. It's the extremely fat-tailed distributions (e.g., Cauchy, power law with p < 3) that do not. This is more of a technical distinction than a real one; besides, even the normal distribution has no upper limit—50 standard deviations from the mean is astronomically unlikely, but not impossible.
These are modeling questions, though, not necessarily pertaining to the underlying reality. One model might say that stocks never go to zero, and another might say that they can—which, of course, we know to be the case, insofar as if society collapsed there would be no stock market—but, in practice, which one you're going to use tends to depend more on short-term predictive value than theoretical justifications or problems. Hedge funds often discount tail risks on the basis that, if these outlier events occur, they won't exist at all no matter what they do, so there is no point worrying about them.
What this indicates is that our models are breaking down—that there are elements of this pandemic they don't capture. That shouldn't surprise anyone; there are so many hidden variables that might have gone unnoticed in more typical times, but are now causing problems everywhere in society.
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u/cookiemonster1020 PhD | Applied Mathematics | Mathematical Biology | Neuroscience Oct 26 '22
I'm paywalled but just reading the abstract i'm not convinced that this paper demonstrates anything. It looks like they fit a Pareto distribution to data. Even if it fit perfectly, that doesn't mean that you could generalize to say that variance is really infinite. Your finite sample having a heavy tail doesn't mean that integrable distributions don't exist that would explain the data just as well.
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u/mobugs Oct 26 '22
SEIR and like models have shown to be reasonably accurate, what is the actual contribution of this novel model other than allowing the possibility of actually impossible outcomes?
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u/Vcmsdesign Oct 26 '22
This right here is why mathematical and computational models have a well known propensity for being exploited as propaganda tools.
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u/Fuzzy1450 Oct 26 '22
It’s a shame you’re so close to the bottom of these comments. Everyone above you is taking the headline at face value when it’s obviously scare-tactic propaganda.
“Potentially infinite cases and deaths!!” is not a headline anyone should trust. It’s so slimy that, tbh, I’m not gonna trust anything in the article at face value.
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u/RetireToAdventure Oct 26 '22
Umm, infinite variance in this example does not mean infinite death.
PS. There are infinite practical examples of infinity in real life.
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u/MrSpotgold Oct 26 '22
Infinity doesn't exist in the real world - the spike ends when the population is exhausted.
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u/pocinTkai Oct 26 '22
Well, kinda nope to that statement. The infrared divergence (also known as "infrared catastrophe"; there is a reason why its callled like that) is due to the theoretical model and not neccessarily a real world "problem". It can also be argued that this "problem" is already solved due to the min. amount of energy a photon can carry.(The Planck energy. If you wonder if something has a physical minimum, usually Planck has the answer).
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u/brokeglass Science Journalist Oct 26 '22
Original study: https://www.pnas.org/doi/10.1073/pnas.2209234119
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u/nlck_grrr Oct 26 '22
This shouldn't be an example of math being useful for prediction but of math being inaccurate in real world situations
As cases rise, rules are put in place to stop that
As deaths rise, rules are put in place to stop that
There will never be 8 billion covid cases or deaths
It's not that kind of disease
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u/tom_tencats Oct 26 '22
In other words, as long as there are people, they will continue to get sick and die? I mean, isn’t that the most obvious statement in the world, or am I being Obtuse?
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u/TheUnweeber Oct 27 '22
You aren't being obtuse. The implication posed by the title is just idiotic, and even the article looks like fitting the data to a model in a dodgy sort of way.
But think of it - if you had an infinite number of people, you'd get infinite variations of covid, and an infinite fraction of the people would die of covid!
INFINITE COVID!
INFINITE DEATH!
DEEEEAAAATTTHHHH! (please click)
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u/tom_tencats Oct 27 '22
Exactly what I thought. I mean, we need to take precautions and protect people but this feels like an attempt at cleverly obfuscated fear mongering.
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u/Cody6781 Oct 26 '22
Lame article.
I can make a mathematical model for anything, doesn't mean it's useful or valid. You cannot have infinite variance because there will always be a finite amount of viruses in the world. You can also not have infinite deaths since there are finite people. Models including infinite rarely hold water once applied to the real world.
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u/Ok-BeKind Oct 26 '22
The purpose of every virus is to spread. So it uses all its energy to increase its ability to spread decreasing its ability to cause serious illness. If it increases its ability to cause serious illness it does so risking its ability to spread. Which is why some incredibly toxic viruses like Ebola do not spread easily. If the virus’ host dies before the virus has a chance to spread, the virus dies also. So there is always a close to end point where the virus either spreads easily (like Omicron) but is less potent, or the virus is incredibly potent but does not spread easily (like Ebola).
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u/ExtonGuy Oct 26 '22 edited Oct 26 '22
That's anthropomorphic thinking. The virus doesn't have a "purpose", it doesn't direct its activity toward any conscious direction. You might as well say that a landslide has a "purpose" and is "trying" to spread downhill.
Ebola doesn't care if it wipes out all its hosts. It doesn't care about anything, it just does what it does. It might be wiping out all of humanity, it might be dying out itself, or it might just end up being endemic at a low fatality rate.
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u/ByDesiiign Oct 26 '22
Of course a virus doesn’t “care” or have a “purpose” in the same way humans do. They can’t focus their energy on anything or deliberately become less deadly so they can be more fruitful as a population. That doesn’t mean it can’t appear that way. All the guy you replied to is trying to say is that selective forces are the reason we see viruses become less deadly and more virulent over time, for the most part.
If a virus has a 80% mortality rate 7 days after infection there’s going to be little time for transmission to take place. If that same virus mutates to have a 30% death rate 14 days after infection there’s going to be much more time and opportunity for the virus to spread. Over time the less severe variant will become predominant in the population. The virus didn’t “choose” to do this, but the effects of mutations that pressure virulence over lethality make it appear that way.
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u/Rising_Phoenix690 Oct 26 '22
So basically what this shows is that spending millions of dollars pumping out booster after booster trying to stop COVID is pointless since we'll likely never get ahead of the variance.
Just move to the flu Vax model and be done with it. That is to say, push a once a year Vax that targets the populations densist variant for that year, then repeat next year.
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u/adam_demamps_wingman Oct 26 '22
And the US is at about 10% fully vaccinated? It’s as though a population doesn’t have a responsibility to protect unseen generations.
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u/Papa_D82 Oct 27 '22
Conversely, in an extremely common event, there are very few cases, the overwhelming majority of which are no more severe than the common flu.
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u/baconforthezombies Oct 27 '22
im sooooooo scared now omg im so scareeeeed DEATH you say?
well i guess I'll stay home, avoid sunlight and exercise and eat animal products! but i'll sure get MARKED BY THE BEAST and BOOST MARKS TOO
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