Ben Sparks explains (and codes) the so-called SIR Model being used to predict the spread of cornavirus (COVID-19).

More links & stuff in full description below ↓↓↓

National Health Service (UK) advice on Coronavirus: www.nhs.uk/conditions/coronavirus-covid-19/

Ben Sparks: www.bensparks.co.uk

Use the Geogebra file Ben created for this video: www.geogebra.org/m/nbjfjtpv

Another good file courtesy of Juan Carlos Ponce Campuzano: www.geogebra.org/m/utbemrca

SOME OTHER RUvidRS ON THIS TOPIC...

3blue1brown on the exponential growth of epidemics: ruvid.net/video/video-Kas0tIxDvrg.html

Tom Crawford on the SIR Model: ruvid.net/video/video-NKMHhm2Zbkw.html

Kurzgesagt on COVID-19: ruvid.net/video/video-BtN-goy9VOY.html

Washington Post simulator: www.washingtonpost.com/graphics/2020/world/corona-simulator/

Extended presentation by Nick Jewell for MSRI: ruvid.net/video/video-MZ957qhzcjI.html

More videos with Ben Sparks: bit.ly/Sparks_Playlist

Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile

We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. www.simonsfoundation.org/outreach/science-sandbox/

And support from Math For America - www.mathforamerica.org/

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Mar 25, 2020

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Numberphile 2 months ago

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

Jonathan Bone Month ago

@nacoran The beta is acutally the number of social interactions. So lets say for example we interact with 5 people. The assumption is that you will continue to have 5 interactions but as the proportion of susceptible population decreases and infected population increases, it is far more likely that the some of the 5 people you meet will be either infected or recovered so the number of new cases declines.

M. Hui Month ago

According to this model, roughly 80% of the population is susceptible?! How is this even possible?? Did I misinterpreted the model or what? Glad if someone could be so kind as to explain this to me!

Christian Evans Month ago

Is there an expanded definition of susceptible here concerning those with weaker immune systems or since WHO declared the youth aren't invincible?

Mahdi B59 Month ago

Please answer this HOW TRANSM=3.2 AND RECOV=0.23??

Jolliebearfor Christ Month ago

REPENT FOR THE KINGDOM OF HEAVEN IS AT HAND!

xin zou Hour ago

i hate assignment

Yash Sehrawat 2 days ago

Which Application are you using??

Lena Araneda 7 days ago

Hi, this might be a really naive question but how can the equations S', I' and R' produce curves if they are linear expressions?

Colin Harris 8 days ago

Can you please provide details of what Geogebra application you use for this?

Hunc HancHoc 8 days ago

22nd May - Perhaps the govt should have used some free graphing software rather than Neil Ferguson's model...

always happy 10 days ago

Awsome explanation. This is exactlaty what I was looking for to help with my diff project

Bedio Soro 10 days ago

What software did you use

Rob Garrett 20 days ago

I like the video but you leave out other variables. What about modeling this disease and using herd immunity as a variable, or put in parameters such as not closing businesses but making rules to allow them to stay open, such as physical distancing within? There are a few states in the US that have done this with minimal to no increase in infection rates.

Badger Beater 23 days ago

Does anybody know, using GeoGebra, how you then integrate these solved derivatives?

David Edwards 24 days ago

This video would have been reasonable if there was a thorough discussion of the assumptions made in the model. But without this it was very irresponsible.

Johann Sedrak 26 days ago

Rest in Peace Sir Conway

Amy Beth 28 days ago

I had understood Rnaught to be equal to transmission rate, not a ratio of transmission to recovery. Rnaught, per my understanding, is the average number of people infected by a person with the illness. (EG - measles' Rnaught is very high, like 13, I think? So one person with measles can infect 13 other people, just on average)

Dee Jarrett Month ago

I got the bit when he said I'm going to use these colours.

Sarath Krishnan Month ago

Please forgive me :coronavirus

Sarath Krishnan Month ago

Show this video to corona virus they will run away after hearing this lecture

Yossi Lampert Month ago

Yeah I can't see the difference between the colors you used but ok I grasped the math nevertheless

Easy Mathematics Month ago

Small "fun fact": In mathematics a "Corollary" is a trivial gift from a theorem. And this word "Corollary" is a derivative from the word "Corona".

BLACKLIGHT Month ago

This is a really nice math video. Special times but nice to see how math is able to predict parts of our world.

Charles Duggan Month ago

Completely off question but what program is Ben using to solve and plot this system of DEs? I've tried GeoGebra, Desmos, and CoClac and even when using the same logic and denomination as in the video, they all freak and act up. I'm trying to do a project which uses a system and would like to see a working plot and equation

David Kearney Month ago

way too geeky

Cooper Gates Month ago

Notice something important and expected, that S', R', and I' sum to zero. I thought he was going to define I' as -R' - S' or the analogous equation for one of the other derivatives.

cena kp Month ago

Thank you for the videos. They are great, you have got a great channel.

Ankush Arya Month ago

wonderfully explained, kept it really simple, I can now implement it in python .. brilliant work .. thanks , hope I could be Mark's student

Peter Vanderwaart Month ago

I have a problem with the definition of S'. If you send 100 infected people out into a population of 1,000,000 people, they will infect the same number as if you sent them out into a population of 2,000,000.

Anjana Ashokkumar Month ago

Fellow mathematicians and statisticians. Please check out our contribution to curb this pandemic. Search for - Team 112 MHRD Mega Challenge. Please watch and like.

Ngocbich Cao Month ago

I hate corona :(

Eraj Qurishi Month ago

what software are u using bro!

thierry dagaeff Month ago

@Numberphile: Dear Numberphiles, I have a demand.. Please, can you simulate the case where, from the peak of I(t) we try to increase transm with time? The challenge is to get a function transm(t) so that the peak becomes a flat horizontal line once it is reached. Interpreting the max of the peak as the number of cases the system can manage (e.g. depending on the hospital capacity), the stake is then to understand how we can go back to normal as fast as possible (increase transm with time) without going over the max. Would Transm(t) be linear, quadratic...?

thierry dagaeff Month ago

And BTW, by keeping I(t) constant at the max for a given amount of time will allow to reduce the length of the tail...

Selim Month ago

great vid but the cardboard background is so ugly

interminas08 Month ago

Tried implementing it in MATLAB (potentially Octave?) Please find the code below and let me know if I made a mistake. N = 1; Istart = 0.01; Sstart = 0.99; Rstart = 0; transm = 3.2; recov = 0.23; maxT = 1; % define S',I',R' % S is y(1) % I is y(2) % R is y(3) %so here fun = @(t,y)[S';I',R']; fun = @(t,y)[-transm*y(1)*y(2);(transm*y(1)*y(2))-(recov*y(2));recov*y(2)]; % Provide the starting parameters Y0 = [Sstart; Istart; Rstart;]; % Define the range of t tspan=[0 maxT]; % Magic happens and matrix Y contains S,I,R [T,Y]=ode45(fun,tspan,Y0); % Plot plot figure plot(T,abs(Y(:,1)),'b-') % S hold on plot(T,abs(Y(:,2)),'r-') % I plot(T,abs(Y(:,3)),'g-') % R xlim([0 23])

KS_NZG Month ago

Hi! I'm trying to use this as a Geogebra lesson in 7th grade and I'm wondering what's the difference of the transmission rate (transm) and the R-nought, you're referring to. Please note I'm Danish, so something might be lost in translation, but as far as I've googled myself into, R-nought is also referred to as transmission rate.

Jade Smith Month ago

Perhaps you should include more variables: economy, vaxinne. From previous models like Mers and Sars, you can some extrapolated values. The longer the lock down, the slower the spread, more job losses and more indirect deaths by jobless people without homes. I think S is difficult to determine as even young healthy people can get sick. S and R are basically each other's mirror image. I might seem to flatten and you can predict the end, but as people see an improvement, they think everything is okay again, which will result in a new spike.

Vlad Antipov Month ago

Thank you for setting this up. I was able to replicate your example in geogebra. I would like to understand how I can inject real numbers into this example. I have a month of real data that I would like insert into this model. The scale for the X axis seems too compressed.

Michael Popovich Month ago

i hate you

LowApe Month ago

Once you've recovered are you susceptible to infection again? It seems that these models assume that you're not, which I don't think necessarily is the case

nab 6215 Month ago

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.

Cassandra Church Month ago

I really enjoyed that, thanks. I’d be interested to see what happens to the curve if variables change over time. Ie, if we stop social distancing at some point.

Yilkal Negesse Month ago

Thank you for your terrific work and clear explanation. But I have question on the way that you calculate the transmission and recovery rate parameters. is there any criteria to calculate them? since I'm working on it and I can't determine them, please help me!!!

Hexanitrobenzene Month ago

You mean fitting this model to real data ? Won't work. It's way too simple. Transmission rate is time dependent due to government measures. Also, I think recovery equation is wrong. As @Erumaaro pointed out, R`=recov * I assumes that recovery is random, i.e., some constant part of infected people recover every day. In real life, I think equation would be R`(t)=integral[ recov(tau)*I`(t-tau) d tau, from tau=0 to tau =t ], where recov(tau) is zero for some 10 days, then gaussian-like for some another 10 days, and then zero for the rest.

CJ Kruegs Month ago

The Coronavirus : *Exists* Area 51 Nerds : *ZOMBIE APOCALYPSE*

Steve Lenores Month ago

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.

John Paul Month ago

I must be reading this wrong! If the transmission rate is pushed up to 10 the peak falls off so rapidly that the whole thing is over in 2 days. Does this imply that herd immunity may actually take place? or is it just that lock down may not work. Could Trump be right?

Rubén Alba Month ago

How to make a model which considers containment measures taken once the disease has begun to grow?

Garima Gupta Month ago

Hi, which software has been used in this project?

Hexanitrobenzene Month ago

GeoGebra. How did you overlook this ?

Z_Krom Month ago

What if the recovery rate is 0?

Axel Andru Month ago

You can't use infection rate data from China. Other countries must eat rats and dogs for the data to be considered.

Benzina Moktar Month ago

What is the software you're using ?

Trade Tech Month ago

Yeah...right..... Only one major problem. These models make absolutely terrible "assumptions" and that IS being seen in just how way off so many 'models' have been when put up against real world data! For example, models don't take into account cultural differences, average age of population & population density per country etc etc. My proof: Compare Italy to Sweden! Massive cultural differences on something as simple as personal greetings, age...(Italy has second oldest pop behind Japan) Now compare Japan to Italy, or New Zealand to Australia, or US to China's obvious BS case figures.... Keep mind here, this virus is essentially the same in every nation. It hasn't "mutated" enough yet to make up for the differences in cases vs actual death rate Another example of some terrible modelling that just made a mockery of it: New Zealand models were predicted to have 80,000 deaths if no lockdown, that was revised to 27,000; then 14,000....and the reality thus far? 1209 cases & 1 death "with" covid19.....NOT "from". That person was elderly and had serious preexisting health issues.... So a mortality rate of .0827

Floyd Barber Month ago

19:25 Flattens the curve by merely adjusting the spatial proportion on the X-axis lol...

Duane Barry Month ago

Thank you, this is wonderfully clear explanation. What happens if the transmission rate is reduced enough to appear to flatten the curve but then is allowed to increase again before 80 or 90% of the population has recovered? Social distancing, if strongly implemented, should stop almost all transmission, but if a large majority of people have never been infected and restrictions are lifted because the curve seems to have flattened (number of cases is decreasing), couldn't the small number of people still infected lead immediately to another spike in cases and deaths?

David Bloomfield Month ago

Hi, Thank you for an excellent video. One comment - whilst "playing" with the variables you run the "infected" curve from peaking at 80% down to peaking at around 10%. In reality, the current worldwide level of (tested) infection is reported as 0.018% and for Spain (one of the highest) 0.3 % of the population. So even allowing for a 10-fold higher number of unreported/untested infections we are still at infection levels of just a few % of the population. So I think it would be better to start with a model running in that regime and look at possible developments rather than show peaks at such high levels as if we were already there.

Jessica Month ago

which Geogebra app is this? I'd love to try this on my own

Benzina Moktar Month ago

I noticed that you can't show the animation of all graphs simultaneously online

Benzina Moktar Month ago

The downloaded app works better than online

Kameron Briggs Month ago

You can do complicated things with math, but its fundamentally simple. I wish more people realized that.

Horinius Month ago

It would have been interesting to plot I+R which is the (cumulated) confirmed cases. That could show people what exponential growth and logistic curve are.

Adam Kučera Month ago

can you debunk evolution using mathemics? look into stephen c meyer for this kind of info

Timothy Douglas Month ago

What about deaths?

Michael Klopfer Month ago

Thanks for this fantastic video to show people the basics of this type of modelling!

M. Hui Month ago

I am desperately in need of someone to explain to me how the values a and b can be found. Many many thanks in advance!

Op Tube - I Support Small YouTubers MarsBat Mapping Month ago

24,024th like :)

Mahdi B59 Month ago

HOW TRANSM=3.2 AND RECOV=0.23????

simplicjusz Month ago

Ben looks like the Russell Crowe of maths!

Val Entin Month ago

It is 'prime', not 'dash'. first derivative of a function is df/dt or f', read f-prime.

Arsenio Buck Month ago

Numberphile = pedaphile

Tab Conwell Month ago

Thanks guys!

Brian Odom Month ago

So flattening the curve, optimistically, we’re looking at a 0.25 infection rate. I live in the United States with a population of about 330 million. So best case, we’re looking at about 82.5 million infections in the United States alone. Wow.

jtcouch Month ago

By treating early, at the onset of fever, coughing and other symptoms, Covid-19 is less likely to progress to pneumonia and is also less likely to invade other organs such as the heart and kidneys. The last thing you want is to wind up in the ICU on a breathing machine. Lack of a quick and easy test has led to 1,000s of needless deaths. That quick test is now available from Abbott Labs, but there remains a distribution problem and a local doctor awareness problem.

Fabian Ram Month ago

what sim are you using in this video

Nicolás Baquero Month ago

Does somebody knows how to calculate the transmission rate from the data of total cases and cases per day? I'm trying to make my own model for my country and I would like to approximate it the best I can. Thank you in advance if someone can help me! Stay safe everyone

Pat Trainor Month ago

Always awesome. But this begs the question, "Where can one get the actual/real numbers of the variables?"

ßri Month ago

You recycled the graph that everyone is using and it tells you nothing about what is actually going on. The only number that matters is the multiplayer and its rate of increase or decrease. Take the number of new cases today divided by the total number from yesterday and you get the daily multiplayer. keep track of that over time to see if you are getting better or worse . in Kentucky we have gone from a .3 multiplier to .14 in the last 15 days so we are getting better even though there are 607 more cases now than then.

FifaKing HD Month ago

Ben used to be a teacher at my school, really nice to see him again!

Miles Pulford Month ago

comes for a coronavirus video nobody: Ben: "differential equations"

ColGadarby Month ago

One thing I have noticed is the number of people in UK classed as totally recovered at 135 against 33,718 total number of cases makes less than 0.5% then I look at South Korea with 5,828 totally recovered against 9,976 making a recovery of 58.4% So surely we should be looking at their protocol and methodology of places like S Korea to see what they are doing right and/or what we are doing wrong. Many countries trying different strategies and some working better than others - this is where numbers can help us. (As @ 3rd April 2020)

Bishop Polycarp Month ago

So, after the lock down when the disease is not eradicated the spike begins all over again? Just delaying the inevitable?

Povl Besser Month ago

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.

Robert Ballow Month ago

inhaling ethanol cures respiratory infection

Nima Nikuie Month ago

Thank you for the wonderful video. What is the name of the math simulator you're using? And is this model predicting that, (short of a cure) 80 to 100% of population will eventually get this virus?

Matthew Acuff Month ago

How about creating a curve that represents what's happening in the real world? Then we'd know the variables--may vary between countries.

Black Knight Month ago

R = resolved would be more accurate and less confusing.

Kevin McCarthy Month ago

Is there a video/tutorial for replicating this work in Geogebra from scratch?

Dicky Bannister Month ago

If you open Geogebra Classic out of the box. the sliders should be on the tool bar. just click 3 of them onto the paper. the 'input' box will be at the bottom. follow the input given that is it. right click on the paper and use zoom. also use xAxis:yAxis to, say, 10:1 (i.e. to get the right relative scale between x and y). that is about it really

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