The Coronavirus Curve - Numberphile

[@numberphile]

Catch a more in-depth interview with Ben on our Numberphile Podcast: kzbin.info/www/bejne/Y6Wqn5xvhMd9jc0

[@TheNecropolis20]

yesterday (July 26, 2021 ) i got my first Corona Virus Vaccination Shot

[@eoghan.5003]

When you can't go outside so you sit modelling death rates to take your mind off things

[@brody5607]

When you can't go outside so watch videos on death rates to take your mind off things

[@biometrix2173]

@@brody5607 when you cant go outside and you watch comments about videos about death rates just to take your mind off things.

[@KazmirRunik]

When you can't

[@Zyphera]

Can't

[@emmanueloluga9770]

C

[@LuganWanian]

Finally a non biased source that Ive trusted for years actually talking about the virus. Yo, I want to express my gratitude for you guys doing this.

[@redtaileddolphin1875]

What biases are you usually seeing when people talk about this?

[@kitkat_ricecat]

Sharing this exact same thought :)

[@bradywells1293]

I know I'm being pedantic, but I think it's important to note they are not without their biases -- no one is. I would agree that presenters on this channel are much more aware and careful of them than other sources, which is probably what you meant anyways =P

[@EebstertheGreat]

@@redtaileddolphin1875 People get pretty political about it, both online and on TV. A lot of people _still_ claim it isn't a big deal and will all blow over soon.

[@ruudbakstra1805]

They should also tell how long it takes.... This flattening the curve will take years

[@josephlucatorto4772]

Can't wait for more geogebra let's plays

[@ACorsaFahrer]

One of the best games ever.

[@brody5607]

It's all the rage

[@juliussoldan4016]

Somehow I find this game harder than Darksouls...

[@PMakerYT]

Yeah the "integral solving" boss had me sweating a bit, but it's very satisfying to beat and then loot all the variables

[@phanthh]

If there was a lets play series on that I would watch it

[@Calber11]

How's the patient? He recovered. So he's fine now? Oh no, he's dead. But you said he recovered!? Oh yes, he's not going to infect anyone else.

[@hhiippiittyy]

I pictured that as a Monty Python skit.

[@amigalemming]

@@hhiippiittyy Wasn't it a Leslie Nielsen film?

[@adriandenson8855]

BEST COMMENT EVER

[@lucasthompson1650]

@hhiippiittyy This is an ex-infected!

[@doriancuculic5825]

So necrophiles are nobody according to your standards?

[@jonopriestley9461]

I think I’ve come to the conclusion that the reason Brady is successful in every channel he runs is because he knows exactly what to ask and when to ask it. Genius!

[@bazsnell3178]

Yes indeed! It's been said many, many times about Brady's videos across all of his channels. He'd have to be a genius to actually understand the Maths, Physics, Chemistry, Computing et al of the subjects he's filming and observing. He knows that he is the voice of me, you, and all of his viewers, and attempts (successfully) to ask those questions that you or I would probably ask if we were actually there in person instead of watching remotely on KZbin.

[@vaged2aj]

yep, it's intelligence, unlike Donald Trump's for example

[@weareallbeingwatched4602]

@@vaged2aj I don't know what descartes would say about trump, but it would not be flattering.

[@DavidKyokushin]

Me : wow, the colors aren't clear. I'm colorblind and it messes me up. ''Ben is colorblind, he has no idea what these colors are'' I feel validated xD

[@robsbackyardastrophotograp8885]

Yep. That was me as a deuteranope watching this.

[@numbr6]

@@robsbackyardastrophotograp8885 I hate the term "colorblind". I see colors just fine. I am R/G "color deficient". I do electronics, can read the color codes on resistors, and such. But I do completely fail the Ishihara color plate number tests. Even the sites that "reveal" the numbers hidden in the dots, the numbers are "gone" when unrevealed. This is very difficult to explain to people with "normal" color perception.

[@tudornaconecinii3609]

@@numbr6 As someone with normal color vision, I sort of got a feel for how it must be like when I failed one question on the Ishihara test. Yes, it might have been only one, but even after I've been told I was wrong and after I knew the answer, I couldn't for the life of me understand where the "3" comes from. So I'm sort of imagining it as that feeling but magnified.

[@stephenwoods4118]

I totally fail the plates, except for the absolute color blindness and the Blue Yellow one (3/15), none the less I have a SODA (Statement of Demonstrated Ability) from the FAA stating that I am qualified to fly at night and under the control of colored lights. This was generated by my going to an airport and having the Tower shine their 'donut gun' color lamp at me with the FAA examiner also watching.

[@blockchaaain]

@@stephenwoods4118 I would love any kind of advice on getting the same waiver. I have put off getting a PPL because I'm afraid to fail and get a permanent restriction. One thing I've thought about it that maybe different types of lights (LED vs incandescent or whatever is traditional) will be easier or harder to differentiate.

[@numberphile]

Be sure to check out the full video description (click SHOW MORE)- lots of useful links there.

[@melon4249]

you should add Medlife Crisis to the description -- he's an authority with a degree and explains it well.

[@wesss9353]

After the 2 weeks, or when folks get out of quarantine, won't it spike up again? A small bump like aftershock after an earthquake.

[@xCorvus7x]

@@melon4249 Or ChubbyEmu.

[@xCorvus7x]

@@wesss9353 In the case of quarantine, if those who recover are immune, then not. But otherwise, yes; the idea is mostly to make the cases happen over a longer period of time, so that at each moment the health care systems will not be stressed that much.

[@360o-j5k]

jeff ross

[@sebastianelytron8450]

*Me:* I'm done with this coronavirus chaos 24/7, I'm going to clear my head with some Numberphile videos *Numberphile:*

[@khangchau9665]

This virus happened large scale in the first place partially bc people underestimated logistic curve and this SIR model so yeah.... math :(((

[@numberphile]

To be fair, we have plenty of standard videos on the way too. Including three crackers with Ben himself that we’re filmed pre-lockdown.

[@cortster12]

Buckle up, because it only gets worse from here. We're likely see cases in the tens of millions before life goes back to normal. Unless some serious containment happens before then.

[@bharatjain839]

@@cortster12 I think government are doing a great job so I guess there would no more further spread but the numbers are going to rise for a certain time until all the the previous already infected people are being tested.

[@xreed8]

@@cortster12 It won't get worse, its been fine this entire time. China and other countries have already stopped it. Why would a mild flu need to stop the world? This event won't even show up on national or global population numbers. I repeat - its a mild virus.

[@logangrove4103]

Ben looks like if Russel Crowe and Andy Serkis had a baby

[@frullo1647]

Big facts

[@frowningJoker]

You should retake your biology exam, two guys can't make a baby. Facts

[@RogerBarraud]

@@frowningJoker Mmmmkkkkay so one of them and the other's sister...

[@deluxeassortment]

@@frowningJoker Two guys can make a baby, with help from a geneticist and surrogate womb.

[@recklessroges]

That doesn't seem relevant to either numbers of philes.

[@jackwoodruff365]

You joke that we are all going to be doing our own models but I am currently writing my masters dissertation on SIR models! Ive been going on about how cool mathematical epidemiology for ages and its great that people are seeing how maths is useful!

[@tear728]

I bought a Springer book on epedemiology and worked out some estimations with the SIR model... it's a really neat area of applied math

[@fouried96]

That's awesome! I did my Honours treatise in mathematical ecology, but I also enjoy the epidemiology side as well

[@gabrielwong1991]

Some economist thinks epidemiology model is a joke, like comparing to DSGE model

[@thedevilsadvocate5210]

A math model does not indicate reality

[@GodzillaGoesGaga]

That's why they call it a model or a toy.

[@tanushagarwal5522]

9:14 petition to have a whole week's course on GeoGebra.

[@liv9589]

+

[@fabiovezzari2895]

I am in

[@vile8366]

Definitely!

[@Diachron]

+1

[@ginatorres9771]

Im in

[@cakes43]

Numberphile: *Decides to put coronavirus in title* KZbin: So you have chosen *_demonitization_*

[@JonathonV]

MadLAd Calib Hopefully not for long. KZbin released a statement the other day saying they are relaxing their restrictions.

[@Jesse__H]

@Robert Coughlin 🙄🙄🙄

[@ichwill7536]

@@JonathonV you have no idea how many times youtubes said things like that.

[@volodyadykun6490]

@Robert Coughlin everyone not liked by me is leftist snowflake

[@z-beeblebrox]

The reason is because any time a major event happens that is likely to generate misinformation or conspiracy theories, youtube automatically combats it by demonetizing those videos and adding an info card beneath them with dry factual information about the event. It works okay-ish for stuff like hurricanes or school shootings, where you get your typical parade of crazies and idiots spouting bad information. But this is not a one-off event, it's an ongoing thing, and a lot of smart people want to weigh in on it, and youtube is simply not sophisticated enough to handle that kind of situation (I mean it's not sophisticated enough for *most* things, frankly)

[@azzyclark3860]

This video has a parker-square level of numberphile production quality.

[@eeli8295]

So perfection?

[@UnknownUser314159]

@@eeli8295 Nope but kinda?

[@bradburyrobinson]

@@UnknownUser314159 - Parkfection?

[@brody5607]

Bradbury Robinson that is a very blursed word.

[@awingding]

Brody Avery It’s a parker-square of a word

[@IndicateADeviation]

So, I'm just a random person that was always bad at maths but found it fascinating. I've been following this channel for a while and I really want to thank you for this video. It's easy to follow even for non maths geeks and it actually might help people understand and also visualize the importance of staying at home and avoiding social contact. It makes the whole 'flatten the curve' policies tangible. So thank you!

[@WYO_BONES]

Differential equations is probably my favorite math discipline. Can really tell us alot about the world.

[@jamirimaj6880]

@@WYO_BONES Almost all of the Millenium Prize Problems involves differentials, they really run the world and the universe!

[@IOffspringI]

In chemistry this is exactly how you would model a self catalysed reaction where the product also decomposes. It's nice to see the math in other applications.

[@NikhilBapat]

im a chemical physics student and was thinking the same! these interactions are like first order unimolecular collisions between infected and healthy molecules.

[@jorgeeduardodussanvillanue46]

Well it's also exponential growth and playing with rates of change, so it's basically analogous. But yeah that's pretty cool about maths, it shows up everywhere :)

[@jamirimaj6880]

Did you honestly expect the maths of other sciences to deviate that big from the original math courses? There's a reason Mathematics is under "Sciences" in almost every universities.

[@lehpares]

Also, I personally consider Numberphile one of the most professionally produced channels in KZbin. The information provided is Top A, Five Class, First Rank quality from experts in the field. What a contribution to the world, Brady.

[@mebamme]

This still feels a lot more like a Numberphile video than a Skype call! Maybe it's the familiar tone of voice.

[@recklessroges]

I think that the video and auto were recorded at each end and masterfully edited together.

[@brody5607]

Christian Stewart Brown paper is magical.

[@michaelgian2649]

@Christian Stewart yup! Brown paper is the meme

[@tjcoding9465]

Brown paper and Brady's occasional comments

[@johnchessant3012]

This was _so_ cool. My jaw literally dropped when I saw "flattening the curve" fall out of those simple assumptions and diff-eqs.

[@A432Hz]

Umbrella Corporation the reason why people listen to politicians is because they’re the ones who determine public policy. Yes, the people should listen to said specialists, but so should the politicians, who are the ones who really need the guidance.

[@willliam1420]

Ergo, what's important is to be able to handle peak infection with serious symptoms at any given time and NOT the shape of the curve

[@willliam1420]

To refine the curve, infected rate shld be further divided into: no, mild and severe symptoms. This alone will flatten the curve also. However it remains that no health care system is designed for a sudden surge of medical care needed for a pandemic

[@davidconsumerofmath]

Umbrella Corporation and the economists too! They’re a kind of mathematician too

[@TheFakeVIP]

This video was just as interesting as any other NumberFile video, keep making them like this while you have to.

[@DaveMody]

I built your model with spreadsheet. Also back calculated the Transmission parameter with the actual population fraction that is infected right now. Thanks for the great video.

[@richskater]

I've actively avoided watching videos about Coronavirus during all this, but I clicked on this one in an instant.

[@AlisonBryen]

Same...because it's based on fact and not supposition and panic. Love Numberphile

[@michelguenette8998]

Raising the numeracy of the public is key. I graduated with a mathematics degree from university, though I have barely applied what I learned doing the kind of work that I did. However, because of that background, I have an ease with numbers and pattern recognition. Being able to play in a sandbox like this should be how the topic is introduced to students who are learning about algebra and graphing rates of change. Thank you for taking the time to make this kind of explanation available. I have enjoyed all the Numberphile videos starting from the beginning when the channel was created.

[@sebastianzaczek]

5:03 missed the Chance to call it "recovid"

[@klausolekristiansen2960]

It would be worse if they had missed the chance to not call it "recovid"

[@groszak1]

REcoveries of COrona VIrus Disease

[@umbragon2814]

He already did call it reCoV!

[@LuisAldamiz]

Thank you, that made me laugh hard! Lungs still working? Check!

[@hamsifardeekay]

5 years of engineering studies, now working in business where + - x / is all I need made me realize I would sweat to solve a differential equation again. Yet this video takes me down memory lane and gives me the strongest conviction that we're doing the right thing, on the 10th day of lockdown here in Paris. Merci!

[@amargasaurus5337]

"all coding has to have really horrible names" That one got me 🤣

[@captainoblivious_yt]

As a programming student, i can confirm that this is true.

[@quasarnova]

Yup yup, just glad he didn't start with underscores and random capitalizations. This is why comments are so important in development.

[@vejymonsta3006]

@@quasarnova Too bad there are many jerks in programming that don't make useful comments.

[@nuno-cunha]

@@quasarnova You should avoid comments in code. Code should be self-explanatory, much like variable and function names... But I much enjoyed the little jab 😄

[@Opamp7]

All code written by scientists and mathematicians has to be horribly named. If your code isn't legible then you ain't a coder.

[@teddyboragina6437]

finally, thank you! You are the math guy, we need you to save us during this math based virus crisis!

[@dantrizz]

Watching this again 2 years on and it feels like the first time round. I knew some maths relating to these sort of modelling techniques from my uni days in Stats and Probability lectures, so when Boris Johnson said around beginning of March that we're gonna go with a herd immunity tactic, my ears pricked up in sheer horror at that idea. And this video perfectly maps exactly why my intuitions were right about that, in a way that is unequivocal in its demonstration what it entails. Thanks so much for this.

[@zlac]

Can you program in "death probability with care" (say 1%), "death probability without care" (say 30%) and "care capacity"?

[@zlac]

Also, it would be cool to have a variable mutation chance based on "people already sick", where mutation could make you susceptible again and stuff, maybe if you had the original version, you're 40% susceptible, but if you didn't have it, you're 100% susceptible and stuff...

[@IgnisDomini97]

@@zlac The COVID-19 virus is currently believed to mutate at a negligible rate

[@andymcl92]

I encourage you to go do it yourself :) Have a play with that model and see what else you can do. You'd need to make a parameter for reinfection, and work out how that interacts with the variables. It might be worth making another variable that's just the sum of the other things, just so you can make sure it stays at 1 (i.e. that you're keeping the population size the same and not accidentally double-counting anyone).

[@tzimmermann]

​@@zlac Actually, there are documented cases of reinfection, not related to virus mutation, simply you may not gain complete immunity from contracting it. Have a look at the SIRS/SEIRS models. To account for disease deaths, you can either estimate the number from the recovered population, or make your total population a dynamic variable by modifying the model a bit. You could then estimate the number of hospitalized persons at a given time by scaling and delaying the infected curve, and once this number reaches the maximum care capacity (number of ICUs in your country), change the death rate accordingly.

[@RBuckminsterFuller]

@@tzimmermann Likely a problem with testing or possibly patients who are immunodeficient in some way. Either way that issue is probably negligible for the model.

[@stevelenores5637]

All models have assumptions which are basically guesses. Computer modelers are modern version of court astrologers. They are no more reliable then reading animal entrails. You never have enough data to make accurate predictions. You occasionally get the shape right but almost never the quantity correct. This what gets officials into a panic taking draconian measures. A lesson for those who too much faith in climate models. Best application for models is preparation but never mitigation. A big key for me above is the sliding bar for infection rates which is BIG QUESTION MARK. It is dependent on other factors like social behavior, the virus itself, cleanliness of environment, and a number of factors we won't know for years o come. Shutting down is not the solution, changing behavior is. Changing behavior will help with every infectious disease not just coronavirus. Of course humans are resistant to change unless they learn the hard way.

[@michaels4340]

Interesting--in America, we would read S' as "S prime" rather than "S dash".

[@oldcowbb]

it's quite obviously a prime symbol instead of dash symbol

[@MrYerak5]

We call "S tag"

[@Jeyzor]

in finnish it would be S comma when translated directly

[@ojjo1892]

oldcowbb it’s quite obviously a prime symbol if you’re speaking a dialect where you call it a prime symbol. In British English it’s not quite so obvious.

[@alansmithee419]

@@oldcowbb it's an apostrophe. "Obvious" to you, only because that's what you call it. To me, there's no such thing as a prime symbol, only something called prime that is often denoted via use of an apostrophe. Oj Jo explained my first point better than I did.

[@jameshart4867]

This 22 minute video about a virus explains differential equations better than an entire year course on them.

[@juangonzalez7011]

Thank you, this kind of analysis really helps everyone understand the harsh measures that all governments are implementing and why it is important that we react on time.

[@LKRaider]

This is a very crude model, it can show the basic concept but cannot inform policy.

[@jamescaley9942]

Some countries don't have harsh measures and have had relatively low infection rates. The harsh measures are based on the idea of eradication, eliminating every single case. How about if it comes back or there is a more virulent strain that emerges? These models are riddled with uncertainty and guesstimates. They certainly don't dictate a particular policy response. There are better and smarter responses than burning down the haystack to find a needle.

[@Joesolo13]

@@LKRaider It can absolutely inform policy. A lower transmission rate means a shallower curve. You can lower the transmission rate by restricting large gatherings, by closing stores, etc. You don't need precise specific values to broadly improve the situation.

[@Joesolo13]

@@jamescaley9942 Depends on what you mean by harsh. Most reactions know full well they will not stop it from spreading, but still follow strict restrictions to do as much as they can to limit it. that's why so many officials are talking about flattening the curve. They know they won't eliminate every single case. No one thinks they will. But aiming to stop it's spread as much as possible can at least slow it

[@drewmandan]

@@Joesolo13 Where in the model is the variable for societal collapse?

[@NoriMori1992]

This is great. There have always been pandemics, but there haven't always been KZbin channels who can show us the math behind them as they happen. And there hasn't always been the technology for those experts to continue collaborating in real-time even in the midst of a quarantine. No one wants to experience a pandemic, but in a perverse way I feel lucky to experience one in this particular decade, where a math channel can keep bringing us content even when they can't get together physically.

[@daniellemacgregor6848]

It is cool to see how 'flattening the curve' works. Thanks for the visual.

[@drewmandan]

Will it still feel cool when you realize that it means being locked in your house for 18 months?

[@ISOwav]

This has been the most useful informational video I've seen on the virus, I understand that as you had said that there are some prerequisites to understand this information, but I wish there was a way this could be released to the common public either on the news, or some other method, because I believe the scariest thing about the virus is that nobody knows what is happening and how it's being transmitted, and personally just getting this tidbit of math based reasoning on how the virus is operating really helped put my mind at ease

[@prime1971]

This has been the single most informative video I have seen on the subject, I'm no mathematition but this explains it perfectly, thank you

[@Thex57]

This is the first and quite possibly only numberphile video I understood exactly what was happening and why. Thanks college

[@otakuribo]

American news: "R nought" British news: "We better call it R zero for the benefit of the Americans."

[@castleblack7382]

Doesn’t make much difference considering they completely misconfigured the R₀ metric. It’s a basic reproduction number where the susceptible populations is always assumed to be 100% and the number of infected 0%. That’s why the slope looked like a smooth rolling hill when he set the R₀ to the current estimate.

[@cybervigilante]

"To be, R Naught to be, that is the question."

[@gamestarz2001]

@@cybervigilante if Hamlet was a pirate

[@john_titor1]

Yeah i don't get it either. We americans use nought all the time, it's how we are taught in schools!

[@lexiecrewther7038]

Anything other than r-oh is fine by me

[@sabriath]

The most important part of that graph is the speed of infection to recovery....because hospitals can only manage so many patients at a time, and only have enough resources in-line production at a given moment. It is very important to "flatten the curve" on the sense that if we don't, then it will cause more deaths just from not having the ability of treatment.

[@greatsaid5271]

let's replace the fear with knowledge

[@Jesse__H]

Or, at worst, let's _supplement_ the fear with knowledge!

[@danthiel8623]

Indeed

[@hhiippiittyy]

@Umbrella Corporation I don't trust you atm. 0.o

[@dizikiwitar6209]

@Umbrella Corporation your name surely fits your coment

[@Mattiaeragiapreso]

Fear keeps you alive as much as knowledge. Knowledge comes from fear.

[@sullyprudhomme]

This was refreshing....no 'fake news' but pure unbiased math. Brilliant.

[@azzaKaiapoi]

One of the best ever Numberphile vidoes, and that's really saying something!

[@MridulKantiRoyChowdhury]

Thanks for doing this in plain speak, making it useful for everybody. With comprehension comes resolution and responsibility. Thank you.

[@yoink6830]

Noticed just now that Ben was wearing a gaming headset. Not to get political or anything, but that's kinda epic.

[@DominicPerry777]

The headsets are nicely versatile.

[@rosiefay7283]

It's a headset with a microphone. Why does it have to be a *gaming* headset?

[@attackdogs3455]

h

[@saintchuck9857]

@@rosiefay7283 because that is what a headset with microphone is called. Historically, low quality audio adequate for gaming.

[@yoink6830]

Rosie Fay It is a gaming product by Logitech and it is a headset.

[@AndogaSpock]

The total number of infected could be off by a huge factor in case of covid-19, as some people get it and show no symptoms, or because there were no tests available, or they didn't want to go to the hospital. This means that you the mortality rate might be much less that the 2s and 3s we have heard in the news

[@Joesolo13]

Yea realistically the infected population is much higher than reported numbers as they're only reporting positive tests for it, and given the shortages of tests in some areas it's hard to properly extrapolate since they're only testing those who have symptoms or have been exposed.

[@robinfleet7094]

Well done. I'm no math genius and this was exceptionally clear and understandable. Some other geniuses need to see this video and get out of the way.

[@h0ll0wm9n]

An informative video! It should be noted that SIR curves can RESET for wide variety of reasons ... perhaps an important one being the virus mutating. The 1918 flu did just that ... into an even more aggressive form. For better disease predictions, supercomputers are employed, which may take into account more variables.

[@TheIdiotsAreTakingOver_]

Everyone is failing to see that the transmission rate will depend on time and on the number of infected people. As soon as the number of infected people decreases from a threshold, quarantine stops and transmission rate goes back up. Similarly, as soon as the economy starts crashing quarantine stops and transmission rate goes back up. What they did was modelling the beginning of the epidemic. That's easy. What's hard is to model what happens when quarantine stops.

[@Hanliu]

That's also what I'd be super interested in. How to implement changing transmission rates? Would this result in a sort of I-plateau?

[@Colony28]

It's really interesting watching how it starts to behave once you introduce some probability of reinfection: S'(t,S,I,R) = -transmission*I*S + reinfection*R I'(t,S,I,R) = transmission*I*S - recovery*I R'(t,S,I,R) = recovery*I - reinfection*R transmission = 1.15, recovery = 0.38, reinfection = 0.03 The system gets a wavy pattern with secondary infection as the R population gets large enough for the reinfected members to matter.

[@costa_marco]

I find that the most pertinent question is actually the units for the free parameters. Brady got it right, but it was forgotten in the video.

[@TacticusPrime]

As long as the units in the parameters match the units in the variables, then it doesn't matter.

[@jakebrowning2373]

Also does it matter what the units are if the ratio R0 is the same?

[@88Xlmk]

Something that many people don't understand - flattening the curve means spreading the cases over much longer period of time, which means social isolation needs to be kept for months. They present it very well.

[@kobold2985]

Watch it come back in 10 years and get everyone who avoided getting in the first time.

[@jamesdriscoll9405]

Those who skip the vaccine, certainly.

[@christianlawrence2714]

10 years? I keep thinking three weeks after the first quarantine break we'll all be on 'day' 7 - 10 all over again.

[@LKRaider]

What Christian Lawrence said, the current models predict we will have to engage in intermittent social isolation for the next 12-18months, being 2/3 of that time in isolation periodically every 2 months. This will be a complete society transformation (avoiding to say disaster, I am hoping we can cope, but not so sure).

[@Joesolo13]

Once the restrictions are lifted it's likely there'll be some level of outbreak as previously isolated people get exposed. So high-risk populations will probably have to self isolate longer if they want to avoid it. The main benefit of slowing it's spread is allowing hospitals to treat all or most of those in danger of dying from it, instead of overwhelming them completely.

[@ruben307]

its unlikely to come back and only affect the people that didn't get it already. I think it is likely that over the threshold of herd immunity number of people will get it or will get a vaccine soon after to be safe. Meaning that others will be able to "free ride" as they say.

[@jacquespansegrouw5513]

This sort of differential equations has various applications in fields of engineering and biology. Cool to see it laid out like this

[@Ovetupp]

Me: Hey, I understand a numberphile video this far! Ben: It's not exactly rocket science. Me: Sure isn't!

[@skullmanjaros]

Incredible numberphile video. I love seeing data and knowledge spreading instead of fear and panic

[@Steve_The_Weave]

Ben mentions whether or not we can “trust” this data being provided to us from other countries, specifically China and/or Iran. This is an incredibly smart man: take his doubts seriously

[@senselessnothing]

Or the US, or the UK for that matter.

[@s3cr3tpassword]

China’s pretty much given up covering up at this point. Comparing the mortality rate between China and Italy the rates pretty much match up. 3% for folks over 60 and 0.2% for folks under 40. So China’s data seems to be true. For now.

[@Mattiaeragiapreso]

He also said Italy. As an italian, I don't know how to interpret that sentence, because a week after we found two Chinese people infected with SARS COV2 , we deleted every flights from and to China while in UK, "doctor" Christian Jensen told that coronavirus was just like a flu and that we were exaggerating, saying that this was an excuse not to work and to do a "siesta", as we always do. A week after that, johnson deliberately said that you had to resign to loose some of your relatives because he didn't want to stop a country, implicitly considering about the 10% (according to letality rates, which would have been equal to mortality rates if the initial idea of Johnson were followed) of all english population as expendable. My country has many, many problems, that's obvious. But you cannot put italy on the same level of Iran and china, which are both dictatorships and the data of which can be easily manipulated to pleasure the regime. That's insulting.

[@Mattiaeragiapreso]

@Raymond Heil this is why every research are published and put to the judgment of other scientists: some days ago a research about SARS COV2 was retired, because it said that the virus can spread for up to 4,5m and stay alive in air for up to 30 minutes. This data were extracted from a case in China, where an infected guy sat on a bus and infected people in a 4,5m range. The scientists that made the study didn't considered that other passengers could already been infected and could not explain why the person sat close to the initial infected subject was not infected. Therefore, this research was retired.

[@Prvosienko]

Probably the best video explanation on virus spread modeling I have seen so far.

[@seanm7445]

Great video. @9:14 if we *did* happen to have the time to learn a week’s course of videos, are there any good resources online for more advanced modelling?

[@brmveen56]

I'm looking forward to this course aswel. 😉

[@sparkytheteacher]

Check @3blue1brown for a fantastic start...

[@jackfroste]

Brady and Ben , thank you for this awesome and very timely video. Stay safe guys.

[@mokopa]

I had Geogebra open when this video appeared on my suggested list :)

[@knightriderultimate]

I did too... And I replicated this, but for some reason the green curve was flat.

[@LKRaider]

KRU's Den the worst outcome of all! :O

[@lehpares]

Superb video! Thank you, Brady, for producing this! I will use this models in my country, Costa Rica.

[@clevergirl4457]

I should get back to my math homework, but i think this is a bit more important...

[@Jitatman]

Ummm you guys het home-homework while at home??

[@senselessnothing]

A bit of a bad idea if you're doing the whisky subjects like cohomology, lie groups and functional analysis.

[@tonyhussey3610]

NO.. The virus will pass...your Education will stay forever...GET back to STUDY NOW !!!!! 👨🏿‍🎓👩‍💼👩🏻‍🎓👨🏿‍🎓👨🏿‍🎓👩🏻‍🎓👩🏻‍🎓👩🏻‍🎓👩🏻‍🎓👩🏻‍🎓👩🏻‍🎓

[@nab-rk4ob]

I got sick. I programmed on the side, but I got sick. Now I do volunteer work. I am learning HTML5, CSS, while rebuilding a 10+-year-old web COPD website. I do stats and charts whenever I can. The lung folks are always Impressed.

[@OJASCKI]

"Make them nice and t h i c c" - Ben Sparks 13:07

[@phanthh]

t h i c c c u r v e s

[@JamesPhillipsOfficial]

Daaaaamn

[@AstroPC96]

Massive respect for using the brown paper..

[@portlyoldman]

That was a really, really useful video. Thanks.

[@wsadhu]

I'm not a detail-nerd, but to get everything straight: the virus designation is SARS-CoV-2 (Severe Acute Respiratory Syndrome - COronaVirus - No. 2) and the disease it causes is COVID-19 (COronaVIrus Disease 2019) ... great video :)

[@wsadhu]

@@00O3O1B thx

[@tnaplastic2182]

Now (March 25): Some people are saying "it is just the flu" or "the flu is worse" May 1st: The same people... "oh"...

[@ItzBirb2]

TnA Plastic nah, they died

[@alphamikeomega5728]

More likely most of them will just forget that they were ever wrong.

[@airriflemaniac]

Your acting like not hoping for the worst to happen, is a negative trait?

[@RBuckminsterFuller]

@@airriflemaniac There's only a problem if hoping for the best prevents you from preparing for the worst.

[@arfyness]

@@airriflemaniac Failing to recognize the magnitude and failing to act to prevent the worst is certainly not a positive thing...

[@lte23401]

Thanks so very much for making the models available to general public, the videos and the links in detailed description section, extremely helpful!

[@ItzBirb2]

This mad lad put Coronavirus IN THE TITLE

[@user-vn7ce5ig1z]

Must be one of the channels that KZbin gave special permission to discuss it and stay monetized.

[@dianav6292]

For the record, I'm an English major and this explanation was very straightforward, even though I'm not familiar with all of the terms :) thanks for the work you guys do!! I wish my math teachers had been able to explain difficult concepts this effectively.

[@nottmjas]

I was expecting the graph to turn into some Mandelbrot sub-set, just like the graph on his video on the variations in rabbit population.

[@centralprocessingunit2564]

lol

[@carlpeters8690]

It would be interesting to see you split the "R" into "recovered" and "removed". It's still all guesses but your video (especially seeing the possible outcomes changing with small changes the variables) was more informative than most of the official presentations I've seen. Thank you.

[@shoopinc]

Excellent, next let's get cliff on the abstract algebra/topology of viruses. Rhinovirus has icosohedral symmetry or coronavirus bobs have helical type of stuff.

[@firstlast446]

Finally an episode of numberphile I can just enjoy without dying from marker on paper noises.

[@rtravkin]

The first time I see the prime ( ′ ) symbol being referred to as a "dash" (normally dashes are these: - - )

[@jamesbrowne1004]

I put this on as something to listen to, as I'm adding today's data. I am running varients of this for our small response team near NYC. I love it as an abstract exercise, but a couple of times over the past few days I've had my hands shaking while working on this.

[@benzeh4769]

I WANT MORE BEN, I LOVE HIS VIDEOS

[@numberphile]

More on the way.

[@noel1637]

Note the hump last longer in time if you lower the transmission rate (not said in the video). Then it becomes worth differentiating between 'removed' and 'recovered' in R. (The model does not do that). In case the cost in 'removed' isn't significant we might question the need to reduce the transmission rate. The cost of transmission rate reduction could become higher than the gain in the removed/recovered ratio. The number of infected (I) does not matter at all. It's the proportion of 'removed' on the green curve that we need to know in order to make decisions on the transmission rate change.

[@garethhanby]

The number of infected is pretty important for countries that do not have infinite medical facilities (i.e. all of them). The main point of isolation if to keep the infected level down to become manageable.

[@MattiaConti]

I hope that this quarantene will finish soon. I'm italian and the situation here is horrible

[@annaliseoconner9266]

I wish you a speedy recovery, both of illness and economy. My thoughts are with you and your country ❤

[@samcooke343]

All of the experts are saying we'll be lucky if it finishes in months, despite what the politicians want to tell us. Hope you're staying safe and all the best, Mattia!

[@tullio9631]

Stiamo inguaiati fratello

[@andljoy]

Take solace in the fact that in Italy your infection rate is starting to slow ever so slightly.

[@Soken50]

Depending on either recovered people can be infected again, how fast the virus burns through the susceptible population and how fast a cure/vaccine is identified and developped, you're looking at anywhere from a few weeks to a few years of quarantine. A few years being worse case scenario where vaccines take time to arise and the virus can reinfect recovered people. Most likely scenario is that recovered will stay immune long enough that the virus runs out of hosts which should take a few month, though that will depend on the severity of the quarantine as well.

[@ZacJelke]

This video is absolutely awesome! I hope this goes trending on KZbin. Most people would probably be bored/uncomfortable with the first part, but seeing the curves explained and how changing that transmission rate REALLY effects things I think it would be helpful for a lot of people.

[@Endermankiller]

There's some kind of ironic nihilism in viewing dead people as 'recovered' :)

[@craighalpin1917]

I shall recover you from your misery with my battle ax

[@alext5497]

This channel owned by China, everyone recovered. You shut now

[@csm8245]

It's basically how the CCP reports from China.

[@vurpo7080]

It's often called "resolved", which is a bit better since it means that case is over regardless of how it ended.

[@BlindManBert]

At 15:25, what you’re seeing is not just the effect of flattening the curve, but herd immunity becoming significant. Here, the number of susceptible people (S) is low enough and the term I/N (the fraction of population infected, in proper unitless form) low enough, that the term transm*S*I/N (properly normalized to units of persons) is so low that more people recover than are newly infected. Thus, the infection is removed faster than people are being infected, and so not everyone is infected. Herd immunity. You can calculate the point at which this occurs, but it’s usually expressed not in terms of these SIR rates but the R₀ value which determines the ratio between the transm and recov rates. I wrote a couple of articles on these points a couple of weeks ago… references available on request but I don’t want to spam the video comments here.

[@KempQ]

Cool dudes, thanks for sharing!

[@Pow3llMorgan]

This is awesome. I think there was a lot of explaining of the inherent assumptions in much of the maths that this channel is about. Like, why does that variable have a negative value, why does that constant have this value, and so on.

[@UMosNyu]

18:20 - I would love to see a graph of people and how they are connected (before and during CODIV-19). How does the number of edges change? mean edges per person/node? etc.

[@shambosaha9727]

Watch Up and Atom's video

[@MrDannyDetail]

It's COVID-19. You seem to be inadvertently conflating it C-diff, which is another nasty bug that mostly affects the lower digestive tract. But yeah it would be interesting to see a video about connectedness, nodes and edges. Perhaps numberphile already has one like it somewhere?

[@michaelgian2649]

Brady, very generous of you to publish this under threat of demonitization by KZbin. I understand they demand the exclusive use of vague innuendo when referring to Corona virus. Hope they don't cut the funds from the entirety of your work. But, then again, no good deed ever goes unpunished.

[@yoavmal]

Ben: I'll make that red Also Ben: Presses brown

[@samarendra109]

1Red 1 Brown

[@benjaminoxford]

Hi all, I just sent something similar on Facebook but I work for the Nhs (not clinical!) and have a bit of feedback/idea. I think you should do an edited/shorted version of this and call it something like ‘The Maths behind why you should stay home’. From 13/14 mins onwards this is a perfect and easy to understand graphical representation of what needs to be understood but you’ll lose people with a 20+ min vid that goes into setting up the model and differential equations. Get it down to the most important info and cut out the too ‘mathsy’ parts of it. Shorten it and get it sharing on as many platforms as possible. Happy to also send to NHS colleagues and hopefully get it trending Ben

[@thulegezelschap5884]

I think “R” would be Resolved, instead of recovered

[@marceldworczyk5726]

Thule Gezelschap thanks for clear up, it’s been bothering me.

[@nopnopnopnopnopnopnop]

3blue1brown explained this really well

[@lukask1800]

Hey Brady, my piece of pi just arrived and i love it!

[@sparkytheteacher]

You can just see my piece of pi on mirror in the background... :)

[@riggdan]

Wow he actually replied

[@tapiomyllarinen1963]

Thank you Ben a man, who really looks like Russel Crowe. I pass this information to my special friends.

[@morpheus2953]

Finally my comp science degree came to use

[@michaeldunlavey6015]

Thanks tons for that. I wrote a little C program and got similar results. I think the biggest concept our "leaders" don't get is the term "exponential". Another way to put it is "doubling time", or better yet "time to grow by 10 times", supposedly around 2-3 weeks. So to go from 1% to (roughly) 100% infected would take around 6 weeks. The more we can slow it down the better, but of course the downside is it takes longer.

[@oliverizzard8751]

We are dying because our “smart” people decided to “question” wether or not chinese data was reliable instead of PLANNING FOR THE WORSE.

[@BlindManBert]

Or we may be dying simply because it’s a lethal virus any way you slice it.

[@jeesimplified]

What software is he using?

[@TheHappyMinecrafter117]

The coronavirus curve sounds like a sick dance move

[@Liam-qr7zn]

17:24 What really scares me about this is how quickly S approaches zero. Most people are going to get COVID-19. We just have to avoid getting it for as long as possible, in the hope that the health-care system not be overwhelmed too greatly.