The MATH of Pandemics | Intro to the SIR Model

How do organizations like the WHO and CDC do mathematical modelling to predict the growth of an epidemic? In this video we introduce the Susceptible- Infected-Recovered or SIR model. This is a simple system of differential equations that qualitatively behalves in a reasonable way. Studying this near the beginning gives a value called R_0 which governs the early growth rate which is exponential growth and is a standard metric in epidemilogy. Indeed real world data shows the current epidemic is well modeled by this kind of exponential growth.

0:00 Assumptions of the SIR Model
3:10 Derivation of the SIR Model
6:44 Graphing the SIR Model
8:58 Finding R0
13:43 Real World Data

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This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria.

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[DrTrefor]

**TYPO** At 5:55 when R' is introduced it should be bI, the same b as showed up earlier, not a new symbol r.
Also, thanks for making this vid go viral, stay safe everyone!

[camelproductions]

I wanted to thank you real quick. I'm working on my Maths IA and this video really helped me understand the topic so thank you very much!

[dharamsarhembram]

when I was teenage I used to love my maths a lot. After spending 4 yrs in Engg. without learning anything I thought that I couldn't do anything. this videos helps me to love maths again.

[gracie]

Hi, I literally cannot begin to describe to you how helpful this video was. I've spent a solid 8 hours today trying to wrap my head around SIR models by reading academic journals but it was as if it was in a foreign language. I'll literally come back to this video to basically write my entire Maths IA for me - I'm trying to model the Ebola outbreak in Guinea. So yeah I just wanted to say thank u smmmm for this you're a lifesaver !!!

[tonymac]

For Chemical Engineers, the SIR model is like when you have A==>B==>C or reactions in series in a batch reactor. Excellent Presentation!! Thanks.

[realbangbang]

Me in 2014: screw this! I'll never use this information in calculus class!
Me in 2020: *taking notes watching this video*

[florinaliu]

I simply think you explain fantastically this issue. I am new scholar in this issue, since i am implementing SIR into social sciences. I was able to understand everything from your video.

[fablun]

This sort of models (ordinary differential equation-based, deterministic approach) are well suited to explain and understand basic concepts and dynamics for ideal cases (uniform homogeneous populations with homogeneous interaction dynamics). This type of models, for instance, does not consider that recovered individuals might infect others or could get infected again. In certain type of epidemics, dead individuals could also infect living ones. A better approach is to consider a stochastic epidemic model considering non-uniform, heterogeneous populations (with subpopulations in mind; for instance, one approach is stochastic network-based epidemics, there are other approaches). The model should also consider measures to fight epidemics to flatten the spread of the infection.

[peterjackson]

Really interesting! I am an IB teacher and I am trying to find ideas for my students Maths exploration

[이재은-qn]

Please don't delete this video. It fits really well with the information I've been looking for. I hope the video that enlightened me is on this channel for a long time. Please leave it😢😢.I'll subscribe!

[kwongkh]

Clear n precise explaination. I m a teacher, teaching Higher School Cert. Exam( Equivalents to A-level exam in UK). I m going to use this pandemic problem but with more simplify modification as a set induction to the topic of different equation to attract students attention.

[atebbe]

This was awesome, as an engineer I've been looking for covid data to play with and these are exactly the type of equations I've been looking for. Thank you!

[ryanjensen]

You rock bro, used your vids almost exclusively for discrete.

[rupe-huzz]

Timely and awesome! I just love this stuff! Trefor just has the knack for clearing the mist on pretty complex ideas. Big Thanks!

[genl]

People often say math is useless and boring. They wouldn't, once they know how to use it correctly for their life better. Thank you.

[damercy]

Such nice explanation. Loved it! It's amazing to learn about new mathematical models, especially when it's taught beautifully like you did. Keep going!

[pt-au-hg]

I won't study calculus even if my life depended on it, I use to say, ... oh, oh, I guess it does, back to studying calculus, my teacher was right, I might want to know this someday, thanks, teacher. :)

[tonyf]

Awesome stuff. I used your videos for Calc II and they helped a bunch. I’m rocking Diff Eq now but I can wait to go back to your videos when I take Calc III over the summer

[neelasingh]

You don't know, but there is an exam called UGEE here, and one of their questions looks directly lifted from your video, now this video gonna help class 12 students also 👍

[duygukorkmaz]

You clear up the main of model. Thanks for your excellent explanation 💐.