The MATH of Epidemics | Variants of the SIR Model

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How do mathematicians model the spread of infectious diseases? My first video on this topic introduced the Susceptible-Infectious-Recovered or SIR model: • The MATH of Pandemics ...
In this second video we look at a bunch of variants of the SIR model. We investigate other stages such as in SEIR model where there is an "Exposed" stage. We investigate vital dynamics, using Vaccines, and the so called SIS model where there is no recovered stage. The initial exponential growth of epidemics can be well modeled by these types of systems of differential equations, but ultimately they are just starting points for the incredibly complex mathematical modeling needed in a pandemic.
Extra reading on these types of models: www.tandfonline.com/doi/full/...
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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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Опубликовано:

31 мар 2020

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Комментарии : 109

@BichoPragmatico 4 года назад

OH, I'm definitely recommending people to come watch this and the other SIR video for further information about predicting models! Thanks for your time sharing this.

@rupe-huzz 4 года назад

Outstanding presentations Dr. Bazett. Just about the best I have come across on RU-vid. Big Thanks!

@UnggulWidy 4 года назад

I am not a mathematics or statistics student, but I can really understand the model thanks to your explanation. Really recommended. Thank you.

@andreasangelou415 4 года назад

I just came to this channel.. Your videos on SIR model are very good!! Nice work!!

@pierrecarrette4976 7 месяцев назад

Thanks a lot Trevor. As an engineer I very much like the adaptations (and so clear explanations thereof) of your toy model to the various practical situations. Kudos!

@ruedigersens9888 4 года назад

Your T-shirt also demonstrates great mathematical insight! Greetings from a german quantum chemist..love your presentation

@DrBiohack 4 года назад

This is really helpful, I've recently discovered your channel and I like the way you present information.

@johannesnakayama5102 4 года назад

Outstanding explanations! Incredibly helpful, thank you!

@HugoFE12 4 года назад

Excelente explicación Trefor Bazett 👍👍👍 saludos desde Bolivia!!! 🇧🇴

@arpitasantra7065 4 года назад

please upload more and more videos on these topic with more mathematical expressions and explanation.i really liked ur video.Thank you

@aashsyed1277 2 года назад

Super exellent + the best explanation!!! Outstanding!!!!!!!!!!!!!

@RealityIsNot 4 года назад

absolutely amazing! Thanks for putting this across

@sekander1253 4 года назад

Well explained, Excellent ! thanks for sharing.

@SHAHHUSSAIN 4 года назад

Grt work sir ...your work is exceptional 😊😊

@theboy7823 4 года назад

Sir can you please make a video on lines and quotient spaces and affine spaces in linear algebra with geometrical explanations. Linear algebra was tough for me, but after I saw your videos I understood the concepts easily. Thank you so much sir.

@karannchew2534 4 года назад

After watching this video... I ordered the same shirt in Amazon.

@GastroenterologyPINNs 2 года назад

It’s a really clear explanation Thank a lot!

@RobbyThinman 4 года назад

Hi. That's fabulous - been hoping for something as informative as this. One question - in a simple SIR model can we make the virus go away totally (i.e. reduce "a" (social distancing etc), and therefore R0) - or can we only hope to flatten the I curve but still have to endure everyone becoming infected at some stage? Many Thanks

@subodhpandey340 4 года назад

Enjoyed alot , thanks for the explaination.

@krenovaFromSG 4 года назад

fantastic stuff. thanks so much for these videos.

@kameraderz 4 года назад

Please cover about SIRU (Unreported) after this one. You're a really great explainer

@kameraderz 4 года назад

@@DrTrefor I find it from this paper www.preprints.org/manuscript/202002.0365/v1, but I can't grasp the calculation 😂

@niki123489 4 года назад

@@DrTrefor can you also add, if possible in next video, how the mass testing and removing people from susceptable category to people under quarantine will affect the equations? Also will people self isolation and people under quarantine will be represented the same way?

@abdohm809 3 года назад

Helpful explanation, thanks

@accountancytuition8542 4 года назад

Excellent video for learners 👍👍👍👍 keep going

@safaumer7826 Год назад

what do d and c signify in the SEIR model? i don't completely understand

@yqisq6966 Год назад

Would be interesting to see if this type of model can have limit cycles - which could explain why we keep getting multiple waves.

@ASHISHVERMA-xh4dd 3 года назад

beautifully explained... and easy to grasp

@DrTrefor 3 года назад

Thank you 🙂

@bijayatapatra826 3 года назад

suppose the mean infectious period for a certain disease is 37 days what is the removal rate if time steps of 1day are used? How I can solve it

@abc_cba 4 года назад

Exactly what I needed !

@danielloh4777 Год назад

So whats does the 'a' & 'b' represent?

@hal511bm Год назад

May I please how accurate has the math been in predicting the course of the current COVID variants pandemics ? What is the first law of logic and math and how does it apply to vaccines and inoculation for HIV ? Thank you if you can answer ?

@bafokengnkone2199 7 месяцев назад

Sir, how would I estimate the constant rate at which Susceptible people interact with Exposed people and eventually become exposed. Would appreciate an answer ASAP

@erict1549 2 года назад

How do you integrate this?

@akimech1 4 года назад

Plz refer literature on these... Very nice video..

@swatimahapatra9806 4 года назад

Sir in the community section you had asked regarding suggestions for starting a new series. I know I am too late for it since I recently got to know regarding your channel but I would like to request can you kindly make a series for mathematical modeling? It would be wonderful learning this topic from you since your explanations are so easy and comfortable to understand from.

@swatimahapatra9806 4 года назад

@@DrTrefor Sir you are absolutely right! I am keenly interested in mathematical modeling but unfortunately I have no resources to learn from. Your teaching is so fluent and easy to understand that I would really love to learn this topic from you.

@swatityagi4358 4 года назад

Very nice video..Can you post a video on bifurcation analysis (hopf bifurcation, trasnscritical) in SIR and SEIR models using matlab and XPPAUT.

@asvintha1035 4 года назад

btw your video and your t - shirt both arer informative :-)

@richardkilliankretzschmar6426 4 года назад

what does the c constant mean

@SaieenTwist 4 года назад

great explanation.

@danielloh4777 Год назад

Could someone explain to me with numbers involved?

@tsatsoulisgeorge6920 2 года назад

amazing video , it would help a lot if you could make a vide explaining the coefficient Ro that we have heard so much about! PS: Where can i get your t-shirt is awesome !

@RLGaub 2 года назад

Thank you for this and your previous video. About to write my SRP (a big project with which we in Denmark finish of our college education, in addition to our exams) and your videos have helped me understand the SIR models and compartment modelling a lot. Definitely going to use these videos as source material. Would you mind if I contacted you, should I have any further questions?

@jakobrasmussen8219 2 года назад

Lol Nice skriver også om det samme, det er bare en SOP i stedet som er det præcis samme bare at andet navn da jeg går på HTX.

@gothicknight5538 3 года назад

I wish people would take the time to watch these videos and understand the complexity and complications of epidemiology. So tired of people asserting their opinions on covid-19 virtually knowing nothing about the subject.

@kerenye955 3 года назад

Nice T-shirt

@ameliarinstone9943 4 года назад

amazing video, amazing **T-SHIRT**

@pravinraut9900 4 года назад

Clear nice explanation. At 11:27, you promised to provide the link for an article mentioning difficulties in building a complex mathematical model for a real situation. Can you please share the link. I would like to read further on that. Thank you!

@pravinraut9900 4 года назад

@@DrTrefor Thank you professor.

@amdtoon 4 года назад

Would you need to represent the dormant time from Exposed to Infectious in any way for SEIR models?

@amdtoon 4 года назад

The lag I mean

@zotac1018 4 года назад

you are god you made this complex topic so easy to understand. Really thanks a lot! keep making such maths videos , i will keep coming 👍.

@bradleyadjileye1202 3 года назад

amazing thank you. Like it

@ahorsucharles7111 5 месяцев назад

Can I get one any where?

@brototodeb 4 года назад

Amazing video, can you add a link to the explicit solutions to these equations?

@brototodeb 4 года назад

Trefor Bazett Gotcha, thanks. Do you have any idea as to the modifications used in the IHME model, I wanted to know the mathematical equation they were fitting all the data against.

@girlthatcooks4079 2 года назад

what happens when the person gets reinfected in the SEIR model after waning of immunity, do we add compartment between susceptible(S) and E(latent) or between R(recovered) and S?

@DrTrefor 2 года назад

I think it’s better to be adding arrows back, not necessarily new categories unless you want things like their subsequent infection rate to be lower

@girlthatcooks4079 2 года назад

@@DrTrefor thankyou so much, where do i add the arrow (between which compartment S and E or R and S) and will waning of immunity be affeted if the reinfection force is reduced by 40%

@reinerwilhelms-tricarico344 4 года назад

What about delays? It should be possible to include in the model the incubation time from being infected to becoming infectious to others. You did that sort of by the "exposed" group E(t). But wouldn't the transition from exposed to infected require a delay term containing E(t-d) where d may be a delay of two or three days? (I'm aware that solving differential equations with delays can be quite tricky).

@reinerwilhelms-tricarico344 4 года назад

@@DrTrefor Thanks - Yes, that makes sense. Delays would be also problematic because then you need also more parameters which are probably hard to come by. It would also make the problem of estimating the parameters from data a lot more complicated I guess. I was anyways surprised that the curves you can find at the Institute for health metric are merely based on curve-fitting with a Gaussian error function. They don't even use any of these models like SIR or SEIR. See: www.healthdata.org/

@argile5 4 года назад

How about a model with two populations separated by water but with airports connecting them. So it would start in one population then spread to the other depending on the rate of airport travel. Basically 2 sir models running with a leakage rate from one to the other....

@altynbekkaragulov5446 4 года назад

You are the Greatest thing since sliced bread!)

@ahorsucharles7111 5 месяцев назад

I really like your shirt and your explanations

@krishnakalakkad2964 4 года назад

If dS/dt is measured in people per unit time, what are the units of parameter 'a' such that -aSI is measured in people per unit time

@hanaazqazi6261 3 года назад

it's just a constant that accounts for things like safety measures.

@taurusdev7965 4 года назад

I see that a is transmission rate What do b c d represent ?

@swish6143 3 года назад

For example a getting better rate.

@elijahmaecabug1890 3 года назад

where can we buy that shirt?

@basic-games621 4 года назад

anyone who did a python code for SEIR with graphs, points and animation?

@JeffreyWhelchel 4 года назад

Add a link to where I can get a t-shirt like the one you're wearing in this video.

@SiyiZhou 3 года назад

oh this T shirt is very cute!

@RobbyThinman 4 года назад

Sorry to be dumb. Your example graph shows 500 "Susceptibles" at the outset and 500 "Recovereds" at the end. However, the maximum number of "Infecteds" only reaches 250? If you are going to have 500 "Recovereds" you gotta have 500 "Infecteds" (at some stage)? What am I missing? Many thanks.

@RobbyThinman 4 года назад

@@DrTrefor Got it!! Thnxalot Trevor. So if an epidemic starts with say 65 million "Susceptibles" and goes into exponential growth, and then (subsequently) we adopt full "lockdown" (to reduce "a"), I would be correct to assume that once the peak in "Infecteds" flattens and then starts to fall we will eventually achieve Zero "Infecteds", but the total number of "have been infecteds" or "Recovereds" can be a lot less than the full 65 million? Thanks again.

@drewkavi6327 4 года назад

How do you solve these differential equations?

@drewkavi6327 4 года назад

@@DrTrefor ok thanks i just studied diff equations this week, is it possible to do these non-numerically

@ahmedmirza1316 4 года назад

Dr. Bazett, Thank you for a not-overly-simplified explanation of the model. I'm an assistant professor of biochemistry but also teach biostatistics. My question, cothata simple or multiple regression model be accurate to predict outcomes? I have developed something that is statistically significant and used it to predict current CoVID19 data from countries that controled the spread of the disease, and it looks pretty good? Could it be published? Or do I need mathematicians like yourself? Thanks

@zerotoinfinity8734 3 месяца назад

🎉

@abanoubabdelmasseh5902 4 года назад

How can I expect the end of coronavirus in my country approximatly??

@Fuzzgun94 4 года назад

Part 1 ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-UW29CGhpkWE.html

@sofiareyes7666 3 года назад

I like your shirt

@feynstein1004 4 года назад

This is why I stick to physics. The models there have very good predictive power without sacrificing simplicity 😏

@martink7609 4 года назад

This is mathematical biology actually. And physics is basically mathematics applied to physical situations. So, you should stick to math instead. Just saying.

@feynstein1004 4 года назад

@Martin K Oh I get that. But pure math is a bit too vast for my taste. I mean, I do admire it and its infinite possibilities that stem from just logic. But I do like being grounded in reality a bit, Which is why I love physics :)

@martink7609 4 года назад

@@feynstein1004 Yeah. So, it's basically like what Feynman said about the difference between mathematicians and physicists. ;-) Cheers.

@feynstein1004 4 года назад

@Martin K Ahaha fair enough

@santoshkumaruppada9498 3 года назад

Sir can I get your mail id once please

@mafarmerga 4 года назад

Can you now please do a video showing how the use of face masks changes the rate of new infections ?

@mafarmerga 4 года назад

@@DrTrefor Yes, I get that. but it would be nice to show with numbers how the rate of infection decreases (and thus saves our hospitals from being overwhelmed).

@KitagumaIgen 4 года назад

*OY!* You should explain that the "constants" for recovery and the other linear transition-terms are "un-biological" since they model exponential loss, which is an ageing-free process. This is clearly not the case in infections. If we look at an impulse-response if infected people (with no further spreading) we would get en exponential decrease of infected. This is not very true to the biology, since it means that the largest number of recovered would recover instantly just after being infected, further too large a fraction would still be infected after too long time.

@ellieli6618 4 года назад

@catnitrom 4 года назад

Is a fundamental mistake in this thinking.. in reality E(t) implies S(t) ..all YOU say is wrong ... U must evolve from „dancing function” to some MATHEMATICS.... try more.. I m so sorry , but you speak so fine with your hands...

@ihbarddx 4 года назад

Ph.D.’s know more about other Ph.D.’s than they know about their subjects. For example, paleontologists know what other paleontologists have said about dinosaurs, but farmers know more about cows than Ph.D. paleontologists know about actual dinosaurs. (And farmers are not given Ph.D.’s.) Similarly, SIR is the way other Ph.D.’s have modeled epidemics, but it doesn’t do a very good job at modeling actual epidemics. (As you point out so well in your video.)

@theultimatereductionist7592 4 года назад

Can't blame paleontologists, since they don't have a living dinosaur with them. That's why it's called RESEARCH: finding out NEW things: not just knowing the old. And you don't know all PhDs, so what a dumbshit generalization.

@ihbarddx 4 года назад

@@theultimatereductionist7592 1) All wonderful points and vulgarities. 2) SIR doesn't model epidemics very well.

@Fynnftm 2 года назад

Umm... what is your point? There's primary research (eg. from taking care of a cow) and secondary research (eg. reading a paper). People in research areas would need to do a lot of secondary research since it is way more effective to learn from what people have already discovered than to start from rock bottom, especially if the topic is very complicated. Researchers build on others' work. The SIR model is a basis for other, more complicated models that epidemiologists use which are more accurate. However, this video is not going into those since you would not understand them (as evidenced from your comment).