Oxford Mathematician explains SIR Travelling Wave Disease Model for COVID-19 (Coronavirus)

The SIR model is one of the simplest ways to understand the spread of a disease such as COVID-19 (Coronavirus) through a population. Allowing the movement of populations makes the model slightly more realistic and results in ‘Travelling Wave’ solutions.

In this video, University of Oxford Mathematician Dr Tom Crawford explains how including population migration modifies the original SIR model. He then goes on to use the results of the model to answer two important questions:

1. How fast will the disease spread? 11:13
2. How severe will the epidemic be? 16:23

The answers to these questions are discussed in the context of the current COVID-19 (Coronavirus) outbreak. The model tells us that to reduce the impact of the disease we need to lower the ‘contact ratio’ as much as possible – which is exactly what current social distancing measures are designed to do.

The third video including an Incubation Time in the SIR disease model is here:

Produced by Dr Tom Crawford at the University of Oxford.

You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths

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[stephenaustin]

Thanks so much for taking the time to do this. It's the first video I've seen which goes beyond a simplistic SIR compartment model, and you made the maths quite approachable. Cheers mate, I appreciate it a lot.

[rumbabolero-taphatunggiaii]

Applied mathematical modelling in action - Awesome!!!

[owenwilliams]

Many thanks Tom, a great insight into how modelling is applied in real life situations. Stay safe.. cheers.

[MrPejotah]

That "I" letter magic @ 08:25

[valoraz]

That’s great Tom, keep on going with these videos

[kalynhowes]

This video is even cooler than the last!

[tomasnavarrofebre]

OMG a travelling wave and epidemics... how lovely!

[johnmorrow]

Great info for those kids AND old folks staying at HOME.

[UnderseaCaveman]

Oh, you're killin' me already (only 1 minute into video). I have ocean engineering master's, and recall "celerity" (speed of propagation). How cool that "Deterministic Wave Theory" has a footing in disease propagation!! Wondering how fibonacci series or more specifically the "Golden Ratio" could play in this....each wave is 31% the magnitude (volume) of previous wave???

[julieolin]

Thank you for your easily understanding math videos! It's a big help!

[ramniergomez]

Great Channel, i learned more about the SIR Model, thanks Tom Rocks Maths

[noonesperfect]

This is some brilliant explanation help me to understand how the model works instead mere exponential growth rate parameter (which is quiet baby in front of this one lol). Again the complexity of these model itself and real life situation which is more complex than model indeed great lesson to learn. Awesome video, you clear the most idea behind it.

Question what is P in S=1-P ? (as Susceptible is now space and time dependent with variable of space "x" and "y" and variable for time is "t" so is it P is particular instance which is nothing but x, y, t dependent in non-dimensional frame?)
Thanks

[victordang]

Is there somewhere to find step for working out of both non-dimensionalisation equations

[Alex_Deam]

One question that I didn't get about the non-dimensionalizing: I can see why the constants r and a disappear, since you wrote them in terms of R_0. But I don't get what happens to the constant D, the coefficient in the diffusion part of the set of equations?

[paulscott]

Great video Tom, thanks. You've got yourself another subscriber.

[supriyoghosh]

Just found your channel, thoroughly enjoyed the video. Thanks and Stay Safe.

[vynneve]

For the second equation after change of variables, shouldn't it be the second d/dy of I, not S?

[Algo]

this was the best explanation as to why we need social distancing I've seen since I even knew that was a thing.

[muesk]

I got a bit lost, new to all of this! From a statistical standpoint, considering we've increased the complexity of the model, we'd expect the travelling wave model to show different (and better) predictions than a regular SIR model?

[PingvinenDk]

Good video - it was easily understandable. Do you have any articles or papers explaining your analysis, e.g. how the minimum wave speed was determined?