The Coronavirus Curve – Numberphile

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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:

Ben Sparks:
Use the Geogebra file Ben created for this video:
Another good file courtesy of Juan Carlos Ponce Campuzano:

3blue1brown on the exponential growth of epidemics:
Tom Crawford on the SIR Model:
Kurzgesagt on COVID-19:

Washington Post simulator:

Extended presentation by Nick Jewell for MSRI:

More videos with Ben Sparks:

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Jeff Potts says:

I did a lookup on the R0 (R-naught) value. The Flu has a R0 of 1.3, COVID-16 has an R0 of 3 – 4. The common cold? An R0 of 6 – 7. This leads to a discrepancy between the model, and historical and known numbers.

I live in the US, so I am using the numbers provided by the CDC, and they are fairly accurate.

In the US, the number of people who will get Influenza in the US is 5 – 20%, so that's 16.6 – 64 million people. In the US some 62 million people will get the common cold. The common cold is a little trickier in that it mutates quickly, and there are several strains that are grouped under the term "the cold," so the number used as an estimate is 1 billion. This is because people will get "re-infected" by the a cold multiple times over the year. But, given the range and the R0 values, the US should see maybe 30 million cases using rough math. So, you're talking, maybe, 30 million people. That's roughly 10% of the population of the US.

Hoang Dong says:

which version of GeoGebra, ad?

Pedro Pinheiro says:

Amazing video, thank you!

Henry Koplien says:

My first guess as I saw the curves of china was, the accumulated infections looks very close to a sigmoid function and I took this approach also with the first derivation for the new infections and tried to find the best fit. Works pretty well.

Fay Ryuujin says:

no doubt Trump doesn't have the math skills to follow this and fell asleep in the first minute or two

Richie Thompson says:

What a bummer! I remember when Jeff Ross was funny 😔

Elaniago says:

Keyword in this video is “naive”, it is misinformation, basically. Guess they wanted to improve their views from tagging the pandemic, which is pathetic.

Viscous Shear says:

funny the modelling is false, way over estimated the problem and destroyed the economy in the process, well played academia looks like you will get your socialism after all.

Andoga says:

Hello Numberphile team, could you make a video about "minimal covering of pairs by triplets" may be work your way up to "minimal covering of pairs by octets".

pujeet jha says:

How would the model change with a virus which transmits even after death like ebola?

Marv3Lthe1 says:

Ok, so the calculus they taught in school are used for these.

fabio silva says:

Why (S*I) instead (s+I)?

Guillermo Fg says:

Thank you, the question is: doint this or that, what the models could say about , how many people are we going to save at the end? (considering colesterol, suicide, vitamin D effects etc of being obligatory at home for 4 weeks)

alvachan88 says:

as far as i have read in the comments, people agree with the flattening of the "infected" curve but no one said a thing about the peak occurring at a later time. IMO, it's better for this to blow up and blow off sooner rather than later so the world can get it over with. less people would lose their jobs due to lower demand so governments won't have to put money into bank accounts of businesses and individuals which might cause unintended inflation. also, people who bought the dip in the market can see the recovery of share prices sooner.

AlwaysHopeful87 says:

I heard that the area where this started in China had a civic function that involved 40,000 people. Causing an alarming infection rate. If models are based on this, the models are faulty. From the NYT of 1/22/20: On Saturday, two days before Wuhan told the world about the severity of the outbreak, it hosted a potluck banquet attended by more than 40,000 families so the city could apply for a world record for most dishes served at an event. On the day it broke the news to the world, it also announced that it was distributing 200,000 free tickets to residents for festival activities during the Lunar New Year holiday, which begins this Saturday.

SimoExMachina2 says:

For someone who studied both information processing and applied mathematics, the starting parameters doesn't seem strange at all. I once made an optimization task for my students, when I was teaching MatLab in Tanzania, to optimize parameters of a SIR model to a given set of data. This forced them to create a model that computes the sum of differences of the model and data with a given set of parameters (the ones to be optimized), and then use the optimization routines in MatLab (a function called fminsearch), to locate the optimal parameters. Really cool stuff, but unfortunately for a class of students attending a basics of MatLab programming course, it proved too difficult. I also did not have enough time to teach them the necessary basics, because of issues of unpredictabilities known as African system. So educationally it was a disaster, but I still love the SIR model.

xMeta4x says:


drgdawson1 says:

I saw a “news” report about how funeral homes were stockpiling caskets for the coming catastrophe. Finally, something that makes sense of this madness.

jull1234 says:

c'mon, just name your variables in a readable way.

graham harris says:

Well done guys.

Mohamed Hmini says:

wow that's amazing!!!!!

kailen haslam says:


macronencer says:

Wow, I had never heard of this app. I must play with it now!

Alex Markessinis says:

Call R resolved.

SJ Park says:

love his enthusiasm lol

S M says:

Can you explain please, why you multiply S*I (and not f.e. S+I) in R` ?

Sylwester Mielniczuk says:

I would skip to 13:19 – ok thanks

Numberphile says:

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