The MATH of Pandemics | Intro to the SIR Model

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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.
PART II here: • The MATH of Epidemics ...
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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Опубликовано:

8 июл 2024

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Комментарии : 498

@DrTrefor 3 года назад

**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!

@siddharthsethia5569 3 года назад

Thank you for the clarification, Enjoyed the video

@surbhi01 3 года назад

excellent video...one query....how are the constants a and b calculated?

@mnada72 2 года назад

I thought that b is different from r because some of the infected are unfortunately dead.

@realbangbang 4 года назад

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

@copernicofelinis 4 года назад

Nothing like dying by drowning in your own fluid can motivate a student more.

@julianocamargo6674 4 года назад

Me in 2014: blah blah blah Me in 2020: OMG, how do I estimate R0 ?!? I NEED IT FAST!

@ralphparker 4 года назад

@@julianocamargo6674 I've been estimating R0 by taking the daily growth rate of the infected (over about a week) and calculating what it needs to be to match that growth rate. But, I'm sure your comment was a jest.

@anadiru4382 4 года назад

not in calculus but you will need this in differential equations

@camelproductions4029 4 года назад

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!

@edayangin7955 4 года назад

OMG ME TOO

@beoptimistic5853 3 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-XQIbn27dOjE.html 💐💐

@jennyzhang2810 3 года назад

heyy same!!! Were u doing hl or sl?

@camelproductions4029 3 года назад

@@jennyzhang2810 Hey! Wow, it's almost been a year now, huh. Thankfully I'm doing SL, I just don't think I would have survived HL lmao.

@jennyzhang2810 3 года назад

lmaoooo im dying in HL, just wanted to ask how did your IA turn out cuz I heard lots of people saying this topic is overused and wont score high:((

@gracie4394 2 года назад

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 !!!

@gracie4394 2 года назад

@Raggul Kanakasabapathy infection rate is mortality rate of disease / susceptible population. i think i really simplified it but my teacher said it was right sooo

@rohinikayal4440 Год назад

Hi I am doing the same, were you HL or SL Math? Would you say this topic was over-complicated or doable? Also, if you don't mind could share some other resources besides this video that you might have used?

@cherylesper7033 7 месяцев назад

hello IB students! same doing my math IA~ it is super hard to read thorugh all those papers, but this video rly pointed out a clear way to success!

@dharamsarhembram9413 4 года назад

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.

@user-tv7jx9pw1q 3 года назад

I studied all possible math modules in my supply chain master and business bachelor, learned a lot of interesting and crazy stuff... But at the end, I don't feel capable to use it properly... But sometimes, like you, I fall back to that love again :)

@kwongkh6880 4 года назад

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.

@rupe-huzz 4 года назад

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

@beoptimistic5853 3 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-XQIbn27dOjE.html 💐💐

@tonymac96 4 года назад

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.

@osculocentric 4 года назад

I work in Quantum Optics, I recently was using similar prey predator lotka volterra equations to predict if the photons will completely transfer to another system :-D.

@sayantanmondal6461 4 года назад

solution of SIR model by stochastic cellular automata ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-cC0JTtKD21c.html

@brett6376 4 года назад

You are so correct. I'm also chemical engineer and I was also thinking of a batch reactor while he was explaining it. He's demonstrating a perfect system. I think I'm gonna check out my old notes and try to use the data that we got from the corona virus. Seeing that I'm in lockdown, I think I gonna try it. Perhaps make a simulation also on chemcad or something

@ryanjensen4232 4 года назад

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

@florinaliu5489 Год назад

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.

@fablun99 4 года назад

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.

@nadija1389 3 года назад

It all makes sense now! Thank you, I was struggling to understand this in my lecture!

@paofmacedon 4 года назад

Thank you very much for the analytical and explicit presentation!

@tonyf1163 4 года назад

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

@beoptimistic5853 3 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-XQIbn27dOjE.html 💐💐👍👍

@atebbe1 4 года назад

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!

@BlindManBert 4 года назад

Austin… You might also want to investigate the SEIR model, which introduces a fourth ‘Exposed’ population representing those folks who have been exposed but are not infectious yet. So the four populations might be termed Susceptible, Exposed, Infectious (not infected!) and Removed (recovered or dead individuals). The aSI/N term is thus subtracted from dS/dt and added to dE/dt, to represent the rate of infection. Then you add an additional rate, let's call it c (or gamma) that determines the transition from E to I, and you subtract cI from dE/dt and add it to dI/dt. Then the final rate of transition from I to R is the same, subtracting bI from dI/dt and adding it to dE/dt. So in summary the new ODEs are: dS/dt = -a S I / N [the division by N is required to get the dimensional analysis right] dE/dt = a S I / N - c E dI/dt = c E - b I dR/dt = b I The addition of the E group lets you model the delay from being exposed to becoming infectious. I’ve read that the incubation period of COVID-19 is averages 5.25 days, ranging from 2 to 14 days maximum. But that is the time from exposure to first symptoms appearing. The time to becoming infectious may be much shorter, perhaps only hours or a day or two (guessing). In any case, the SEIR model is more appropriate when there is a delay from exposure to infectiousness. And then you can do all sorts of fancy things like representing age groups in different pools with different transmission rates between the groups, illness times, time before isolation (removal), age dependent mortality, and so on. I wrote up a survey of mathematical modeling techniques including the SIR, SEIR, and actor (stochastic) models on the ScienceVsUniverse group on Facebook, which I can’t directly link to here. But if you look for “A partial survey of epidemiological models” you’ll find that article with links to a few good pro-grade SEIR and actor models. I also maintain via the same group a public-domain OpenOffice spreadsheet where time-series CDC data can be extracted, or you can use time-series data from the John Hopkins University CSSE GitHub site, or CSV files you can download from OurWorldInData(dot)org as the time-series data. I find it helpful as well to pass the time at home running models to double check the ‘sanity’ of models thrown about in and outside of scientific circles. Good luck!!

@peterjackson7348 2 года назад

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

@user-yf1ep9zo8r 7 месяцев назад

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!

@Anooshehk 3 года назад

I absolutely love your channel. Thank you so much.

@krisellcainicela129 4 года назад

Gracias por la explicación, fue estupenda !, amé esos subtitulos!

@marwanbasem193 3 года назад

Really thanks for that amazing video, I've never dealt with modelling before but you made it so intuitive. You also encouraged me to try and add some other factors into the model, like the effect of vaccination. Thank you so much.

@elderaarondavis1 4 года назад

Wow. As an Econ major, we use partial derivatives and DE in our model too.

@falehalyazidi956 4 года назад

I’ve been reading to understand this model and clear all misunderstandings. However, your way of presenting this model, the content and examples were very beneficial and amazing. Thank you very much..

@beoptimistic5853 3 года назад

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@damercy 4 года назад

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!

@beoptimistic5853 3 года назад

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@arunhuddar 4 года назад

Excellent explanation. Did not expect Maths to be helping saving lives.

@gen1l 4 года назад

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.

@neelasingh9578 4 года назад

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 👍

@denisbaranoff 2 года назад

Awesome deterministic version! Awaiting for stochastic 😊

@duygukorkmaz9433 4 года назад

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

@beoptimistic5853 3 года назад

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@ElPasoJoe1 4 года назад

Really good video. Gonna go back and watch the video, take notes, and fill in the details...

@FloriUchiha789 2 года назад

You're the best, thank you for the big help!

@asherstackhouze1107 4 года назад

More clear than my teacher does. Thank you sir.

@xmaster622 3 года назад

Hey joe I gotta love your life I

@mishasulikashvili1215 3 года назад

Thanks for great video, Trefor ❤️

@user-pt-au-hg 4 года назад

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. :)

@maurocruz1824 4 года назад

The explanation of the R_0 is brilliant. Thanks professor.

@marvellousolatunji9719 3 года назад

Interesting video, Kudos. I look forward to other videos on the model.

@AntonyDova 9 месяцев назад

Thank you so much sir!

@giacomogavelli4095 4 года назад

It is a pity a lot of people are afraid of mathematics almost as they are afraid of this Virus. Having the interest and the capability (which for me is relatively low) to understand this approach help me a lot in being aware of what is happening around me. I'm from Italy (and I'm sorry if my English is not so good) and I'm seeing a lot of people that don't understand why some precautions are taken and they think we are all going to die. P.S. thank you for the video. The content is very well explained

@thevapingpig 4 года назад

I'm a Canadian, the whole western world is in panic. We watched the growth, while our politicians for the last couple of months this thing was growing have been fucking around. Now we are in a situation where we are watching it explode in our country, but we've all went under mass quarantine to try to decrease our transmission ratio. I've been obsessed with learning the modelling and try to make my own predictions for how it'll effect my city, and country. Hope everything eventually improves in your country, people over here are super scared of calculus just like this virus.

@floridaman318 4 года назад

You're English is actually fine. What's most frustrating about this virus is the ignorance, if not downright arrogance, displayed by so many people. If they understood how damn cost effective it is to actually aggressively contain an outbreak in its early stages, they wouldn't be worried about "looking stupid" or "falling for the media sensationalism." You guys in Italy will be getting better in coming weeks, you huys reacted almost a month quicker than us. The US numbers aren't looking good.

@BlindManBert 4 года назад

@@floridaman318: I’m just chuckling at “You’re English is actually fine.” [English language tutor; not a grammar Nazi.]

@floridaman318 4 года назад

@@BlindManBert for a non native speaker, yeah. I've seen much worse writing from native speakers.

@BlindManBert 4 года назад

@@floridaman318: It might be that you missed what I was chuckling at; the choice of “You’re” as opposed to “Your.”

@23andrelopes 3 года назад

Such a great video

@Leila0S Год назад

I like you Dr. Your dedicated explanation is attractive. The more I meet PHDs, the more I am convinced I must go for it.

@ismaelabdulrahman7295 4 года назад

I really like the way you showed the problem. I enjoyed the video. Thanks.

@beoptimistic5853 3 года назад

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@biaschatterjee9836 4 года назад

I was trying to understand this model, your video made it crystal clear. Very helpful, excellent video. Definitely gonna watch your all videos 😊👍👍👌👌

@abraga123 4 года назад

Excelent! Thank you very much.

@ekwan16 4 года назад

Thanks for a very clear introduction!

@beoptimistic5853 3 года назад

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@alexz2411 2 года назад

Great Video

@maxdemuynck9850 4 года назад

great video! really interesting and informative

@osamaagamirashwan4783 4 года назад

Thanks for letting me know different application for the system of first order DE as I use it in the circuit with loops including capacitors, coils, Resistances, and DC source.

@beoptimistic5853 3 года назад

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@sanjaykrish8719 2 года назад

I never expected a diff eqn being formulated, though i hv solved many. Math is nice

@8829david 3 года назад

There is one thing at 4:50, is not more probable to get infected if S=10 and I=100 than if S=100 and I=10 Because 100 infecteds will infect the last 10 non infected with a more probability than 10 infected to infect the helthy 100 but the rate is the same. Same happens in chemistry with rate of reaction in kinetics that each concentration is powered to some exponent

@terrywang7984 4 года назад

Excellent, informative, and clearly explained. Subscribed

@Jabert0001 4 года назад

awesome explanation, thank you for this video.

@beoptimistic5853 3 года назад

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@francaciari944 3 года назад

Beautiful video. Thanks !

@beoptimistic5853 3 года назад

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@SareBear2000 2 года назад

Nice, I just read an article on the SIR model

@aapsarna4198 3 года назад

Thank you sir

@brandonkim4920 2 года назад

This was very helpful. Thank you so much for making this wonderful video.

@DrTrefor 2 года назад

Glad it was helpful!

@hereusername 4 года назад

awesome video

@aibee5794 4 года назад

Thank you Guruji

@thiagocastrodias2 4 года назад

I loved the video, but I think I should watch it again some times to better understand it. But it's very fascinating for sure

@sayantanmondal6461 4 года назад

solution of SIR model by stochastic cellular automata ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-cC0JTtKD21c.html

@MrFranciss 4 года назад

Thanx for you great explanations. I could understand everythingeven with my arts formatted brain.

@MrFranciss 4 года назад

Lol, in the next life maybe.

@probablyaxenomorph5375 Год назад

Working on a calculus final project that talks about how calculus applies to epidemiology... can't help but be depressed by all the "here's what hopefully won't happen" talk when we're three years into the pandemic.

@pipertripp 4 года назад

This is great. I'm just starting to teach myself ODEs and this vid was a nice presentation on a practical (sadly) application. Talk about being relevant...

@pipertripp 4 года назад

@@DrTrefor for sure. I bought Boyce and Prima back in early march and I'm currently in chapter 2. I love modeling stuff with python so I already have a little bit of experience with numerical techniques (Euler-Cromer). I'll definitely check out your content. The text book is really excellent so far and I love the fact that both odd AND even number problems have solutions in the back. That's very helpful when working in isolation. That all said, content like your and others is essential as you guys kind serve like the tutor who puts things into conversational english and you provide a lot of context... that is something that I think is under appreciated in science and maths education. I find that concepts and information sticks with me much better when I already have some context in the subject in question. Thanks again. Without people like you, my road would be both rougher and steeper.

@josephacolletti 4 года назад

Bro, very nice on many levels. Format/style, info, clarity, simplicity ... you’re a genius

@andrenuber8852 4 года назад

Great video that lets me understand how to get to the basic equations. Furthermore, you clearly demonstrate the connection to the exponential growth. Don't know if someone mentioned it before: Why do you use another constant (b) for the lost infected people than for the gained recovered people (r)?

@alexdabruh 4 года назад

Thanks Trefor, I missed your MAT223 class back in UofT

@alexdabruh 4 года назад

Trefor Bazett Lol, if it is in the 2016S semester I might be in it

@taibimath7092 Год назад

goooood presentation

@spicemasterii6775 4 года назад

Amazing video. Amazing explanation. Subscribed!

@beoptimistic5853 3 года назад

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@johnmartin7346 4 года назад

I think there is a stochastic variation of SIR model. It would be fine to see something about that. Thanks.

@TheLvpatel 4 года назад

great video

@Joscquin 4 года назад

Hi, and thank's for this video. I just uploaded a french translation, which I hope should be available soon.

@Joscquin 4 года назад

Your video corresponds exactly to the mathematical level of my biology students, but their english level could prevent them from understanding everything. I'm sure they will be very interested in your video, as we in France have a very serious situation concerning Covid19.

@MardkoMBR 4 года назад

Joseph Nicolas, merci beaucoup pour la traduction en français !! P.S. Spain, where I live, as a much worse problem with Covid19 than France unhappily. Once again, thanks a lot for your translation. Keep safe !!

@dr.natrajdravid7786 4 года назад

Beautiful.

@melkdoria 4 года назад

Very clear and pleasant exposition. More could have been done, though 15 min is not enough and shouldn”t take longer. The singularities and the death could have been explored. Great job👏

@beoptimistic5853 3 года назад

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@MrArunavadatta 4 года назад

Well explained..Thanks

@roddiepiper5559 4 года назад

The term "-bI" seems rather simplistic, as it assumes that a constant percentage of sick people will get well or die on any given day. Most acute illnesses seem to run a fixed-length course, so in a more realistic model, some percentage would die two weeks after infection and the rest would recover three weeks after infection. E.g. dI/dt = a*S*I - d*I[t-14] - (1-d)*I[t-21] where d is the death rate and I with a negative subscript is zero.

@mohammedmalik7992 4 года назад

Very informative. Thank you

@beoptimistic5853 3 года назад

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@presse55 4 года назад

Awesome presentation! Ron from Montreal B.Math 78!

@abhishek_raj 3 года назад

Ohho So its all being done to lower R0, got it !

@ralphparker 4 года назад

12:10, regarding coefficient b. If you consider recover more than getting well, but removing an infected person from the ability to infect others, then quarantining effectively increases b. Maybe a better term would be considered in this thought. In my thoughts, and attempt to model this epidemic, recovery is not proportional but a delay. That is, those who were infected at time T recovered at time, T+R_t, where R_t is recovery time or time that the infected person is removed from the infected pool. I would really like to see what the CDC and upper echelon Health experts are doing in their models.

@jiteshbohra6164 4 года назад

Great video

@josesantiago959 2 года назад

te amo wey, me enseñaste más que mi profesor.

@imanelshair7746 4 года назад

very informative and clear explanation , thanks a lot

@beoptimistic5853 3 года назад

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@holysong2099 4 года назад

The model is very nice sir but since it assumes that all people are allowed to meet each other without any restriction (S multiplied by I) throughout the epidemic, it makes every person to get infected at least once and then recover. IMO It would be more reasonable to call the third category as 'non-susceptibles' or N(t), so that now susceptibles,S(t) can directly jump to N(t) without having to cross the infection stage(through vaccines).

@gaeb-hd4lf 4 года назад

Good point, does such model formally exist? Cause it seems a pretty important parameter to me...

@mcarleton 4 года назад

It is also said that nobody is immune to the virus, since it is noval. I expect that there is always a very small number of people in the population who happen to be immune just due to the variation of the genetic makeup in a large population. The recent pair of people who were cured of HIV had bone marrow transplants from someone who was immune to HIV.

@batnav10 4 года назад

I would also assume there have already been a small part of the population in the world that were already infected and either recovered or died from this virus before it was declared a pandemic or widely known about beforehand.

@ahmedmagdyghouneimy7574 4 года назад

Wooooow ♥ You make things intuitive. Thank you so much for this fascinating video!

@johnnysparkleface3096 4 года назад

I would give anything if I could understand just a tiny fraction of what he said.

@beoptimistic5853 3 года назад

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@Laowu1898 4 года назад

great work！

@iarasouza8029 4 года назад

Amazing!

@beoptimistic5853 3 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-XQIbn27dOjE.html 💐💐

@pikapuff123 4 года назад

Hey Trefor, I'm really loving your content! Could you really briefly describe you process for making these videos: programs you use for generating the png plots and overlaying all of the elements of your videos. Thanks!

@jboushka 4 года назад

I think Peak Prosperity's videos have talked about some of this.

@YOURFRIENDMATHEMATICS 3 года назад

Nice communication skill. I fully support you. Lets grow together

@niki123489 4 года назад

when the numbers of infected people in China started to raise I immediatelly start thinking about the differential equetions about the rate of change of the number of infected people over time.

@0xsuperman 3 года назад

I'd like to ask a few follow-up questions. 1) For forecasting future cases using the SIR model, do you try to fit the SIR curves with existing, actual data? If so, what systematic approach or evaluation standard is accepted to identify the parameters which give the best fit? 2) How do you incorporate additional information/variable into the SIR models? I.e., if lock-down happens between day 20 - day 60, and the SIR curves are affected by it, is there a way to incorporate this lock-down variable so that we can estimate its potential impact into the future? Please explain or if you know any textbooks/papers, I will be appreciated to dig deeper.

@GeneralApocalypse 11 месяцев назад

I am working with this model for my college project

@igoralves1 4 года назад

In 2:33 at time Zero we should have So=N-1(Population minus the zero case or first infected), Io=1 (first infected -> mandatory), Ro=0

@radio2712 4 года назад

It is really a nice video😀😀

@BlindManBert 4 года назад

At 7:30, there is an assumption stated that everyone will eventually become infected which is not entirely true. For aggressive values of the ratio R₀=a/b, that will certainly be the case. But not so for values of R₀=a/b just above 1. So, for example, I have a SIR model loaded in GeoGebra with the identcial ODEs and I can set a=0.45 and b=0.3, and initial conditions I₀=0.01, S₀=1-I₀=0.99, and R₀=0. At t≥50, the system settles down with near 0% infected individuals, 40% susceptible and 60% removed (aka recovered). This phenomenon is due to the fact that herd immunity will set in when enough susceptibles have been drained to make the infection rate start to fall off quickly. It is true that dI/dt doesn’t ever fall off and become zero… it continues to shrink indefinitely to whatever numerical precision you care to use. But in this scenario it can’t impact the S(t) and R(t) values significantly, and they stabilize at midpoints rather than always asymptotically approaching 100% and 0%, respectively. You'll find my model on the GeoGebra(dot)org interactive website as "Simple SIR Model (based on Ben Sparks' “SIR Model”)". Should you wish to build the same model using GeoGebra (a free download) here’s the source code for my GeoGebra file. I’m am using here ‘a’ instead of ‘β’ (beta) and ‘b’ instead of ‘γ’ (gamma) to match Trefor Bazett's rate parameters. But other than this naming change, my GeoGebra file is identical to the source below. N = 1 a = Slider(0,5,0.01) b = Slider(0,5,0.01) T = Slider(1,100,1) I_0 = 0.01 S_0 = N - I_0 R_0 = 0 S'(t,S,I,R) = -a S I / N I'(t,S,I,R) = a S I / N - b I R'(t,S,I,R) = b I NSolveODE({S', I', R'}, 0, {S_0, I_0, R_0}, T) After you type in the NSolveODE, GeoGebra creates three equations with new temporarily named variables. The last step is to rename those temporary variables and change the X:Y aspect ratio to 10:1 or 20:1 and you’re good to go. R_t = NSolveODE({S', I', R'}, 0, {S_0, I_0, R_0}, T) I_t = NSolveODE({S', I', R'}, 0, {S_0, I_0, R_0}, T) S_t = NSolveODE({S', I', R'}, 0, {S_0, I_0, R_0}, T) That’s everything!

@feynstein1004 4 года назад

Great video, subbed :)

@amitabharolkar3560 4 года назад

Very well explained 🙏

@beoptimistic5853 3 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-XQIbn27dOjE.html 💐💐👍👍

@sjj_02 4 года назад

What a great explanation! So can I use this video as a reference for my high school assignments?

@kristiansvendsen6549 4 года назад

Is "a" the chance of a meeting leading to the susceptible to get infected? And in that case, is a=I/N ?

@chmeland 4 года назад

Great video. I stumbled over it in my search for how to calculate R from the growth factor. Could you explain that?

@beoptimistic5853 3 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-XQIbn27dOjE.html 💐💐

@finn8205 2 года назад

Epic thankyou

@FrankNestel 4 года назад

Increasinc b means developing a therapy (treatment, medication) for the sick.

@BlindManBert 4 года назад

Actually, once a person is hospitalized or under a doctor’s care, one would presume that they are already self-isolating. So really the b parameter shows how long it takes from becoming infectious to not becoming infectious; it could simply mean that they are under strict quarantine and the risk of infecting others, like medical workers, is quite low as opposed to walking about in the population. The b parameter can be increased through early detection; regular temperature testing at checkpoints or at home, broader testing regimens, etc. For SIR modeling, what is significant is when a person is “removed” from the infectious population, not when they recover. SIR is often used to imply susceptible / infected / recovered (or dead) populations, but the better words to keep in mind are susceptible / infectious / removed. So too, there is a related SEIR model to allow a timeframe, usually a day or two, from an individual being exposed (the E) to becoming infectious (the I). We know that for COVID-19 there is an incubation period of about 5 days on average, ranging typically from 2 to 14 days, from exposure to becoming symptomatic. But a person might be shedding quite a lot of virus within a day or two of being infected and asymptomatic. And then typically if they are sick they might change their habits or go under quarantine a day or two after developing major symptoms. But yes: the goal of everything we should be focusing is reducing a and increasing b as much as possible. Put together, that’s how you pound the curve down into exponential decay as opposed to exponential growth or a steady state.