Just to clarify, the idea of this video is to inform people about how maths is used to model disease spread and to show why social distancing is SO important in reducing the impact of an outbreak. I am not giving medical advice, just informing you all of some of the background behind the advice given by the experts. Stay safe everyone and remember to keep your distance.

@dptirkey

4 жыл бұрын

This model is then simulated using system dynamics software like Vensim , or there are other softwares the Government uses ?

@TR4zest

4 жыл бұрын

Tom: thank you for this. I am no mathematician, but you helped me understand the model. Good work.

@JohnDlugosz

4 жыл бұрын

@@dptirkey See Numberphile's new video for solving and animating the curves. They used a free program called Georgebra.

@UsmanAli-yo3nc

4 жыл бұрын

Thank you so much Tom. I am a medical doctor and hence do not have much understanding of mathematics. I think your video is best to explain the SIR model and it's formulas on KZread. I still cannot understand the concept of IMAX calculation and R calculation. Can you explain it a bit more that how log comes into play? And how equations are derived. Secondly any suggested readings for beginners like me? Million time thanks.

@jarsoabdulkadir7801

4 жыл бұрын

Thank you.

If machine gun kelly pursued maths instead of rap. Thanks a lot for the video, helped me with a report.

@TomRocksMaths

3 жыл бұрын

I'm listening to his new album on repeat at the moment - loving it!

@a_green_cat

3 жыл бұрын

Haha i was thinking the same

This video is great and the material is explained so well! This is exactly what I needed for my Calc III report on COVID-19. I'm glad to see some "real" math rather than the same graph showing the "flattening of the curve" over and over again.

@TomRocksMaths

4 жыл бұрын

Thanks Kalyn - glad it was helpful!

Part 2 on extending the model to include the movement of populations is here: kzread.info/dash/bejne/p4eAqNede6XUcqw.html

@abhiroopreddy8673

3 жыл бұрын

Hey tom how do we calculate the transmission rate? and if so, what is the rate of contact/transmission rate for current the current COVID-19 pandemic?

Hi, I'm S. Korean Highschooler and honestly respect you. This was much significant to me.Thx

@TomRocksMaths

4 жыл бұрын

You're very welcome.

Thank you so much for sharing understanding and reason in this absolutly crazy time. Best wishes to you all from Munich :)

I’m so glad you are here. Stay safe, spread the math word. Thanks so much. Minnesota, USA

Hi Dr Crawford, I've discovered your channel recently and, as a maths fan, I wanted to say that I think you did an amazing job at explaining the SIR model in a clear and understandable way. In fact, I've liked this video so much that I decided to add Italian captions so that I can share it even with people here in Italy who don't understand a lot of English. Hopefully my captions will soon be available and other languages will be added too by other people because I believe your videos deserve them :) (Also perhaps I will add captions for other videos of yours soon )

I used the statistics on the values of S, I, R, and the changes in S, I, and R each day, and plug it into the SIR model, and the current estimate is that the total number of infected individuals (I + R) can reach *a quarter of* the world population. We do need to decrease the value of R_0 drastically to stop the spread of the disease. Great video with a great message!

@plrc4593

4 жыл бұрын

How did you use SIR model since real I and hence also R and S are unobservable?

@mathemaniac

4 жыл бұрын

@@plrc4593 I simply used the data of reported cases from Worldometer. See the spreadsheet linked in my latest video for more information.

@plrc4593

4 жыл бұрын

​@@mathemaniac But how did you use them? If for example Italy reports today they've got say 1000 new cases it means those patients fell ill say 5 days ago, not today :D And they infected other people throughout all these days. Moreover they're now in hospital so they're removed from the system and don't infect other people any longer. Other than that in addition to those 1000 known cases another say 10 000 people fell ill 5 days ago but simply didn't present symptoms. But they still infect other people. Did you think about all these questions? :D I bet you didn't.

@mathemaniac

4 жыл бұрын

@@plrc4593 It's not that I didn't consider these. There are lots of caveats shown in both the pinned comment and the spreadsheet, which include some of your concerns (maybe you haven't checked those out?). This is kind of the limitation of the SIR model though. It assumes quite a lot, so that we can get the big picture as well as making it easier to understand.

@plrc4593

4 жыл бұрын

@@mathemaniac You mean this spreadsheet: docs.google.com/spreadsheets/d/14XWEmLefkh-jRiHMeWc8kvM3sk9Q-Mx4EYHHlOSC_1Q/edit#gid=1994039230 ? There is no formula. At least I don't see any. Just few sentences.

Thanks so much for sharing your expert knowledge with general public!

this video is pure gold, my final exam was an sir model based project, and your video helped me a lot

@TomRocksMaths

3 жыл бұрын

Glad it helped Tobias!

Differential algebraist here! Our entire lives/careers are devoted to searching for exact solutions to systems of differential equations like the SIR model!

Brilliant, very accessible explanation. Thank you!

Thank you so much for this! I happen to have been given a class project to evaluate the SIR model and this video was incredibly helpful - thank you again!

@TomRocksMaths

4 жыл бұрын

You're very welcome Leanne!

I was just building an SIR model to fit the parameters for COVID-19 in python! Fantastic video

@plrc4593

4 жыл бұрын

How did you use SIR model since real I and hence also R and S are unobservable?

@montanariarthur

4 жыл бұрын

@@plrc4593 S and R are actually observable variables (assuming you have a reliable measure of I)

@plrc4593

4 жыл бұрын

@@montanariarthur Hehe "assuming" :D

@montanariarthur

4 жыл бұрын

@@plrc4593 Well, the system is still observable, the problem is that a Luenberger observer is not going to asymptotically converge to the true value of S and R!

Thank you !. Could not have done my assessment without this video.

thank you so much for making this video!! i was really interested in how the COVID-19 outbreak could be modelled, and as someone who recently finished differential equations in A Level Further Maths, your explanation was great and i enjoyed following along!! it's keeping me into maths while college is shut :)

@TomRocksMaths

4 жыл бұрын

Awesome - I'm glad you enjoyed it!

I’m in love with Tom , he rocks

Thank you very much! I finnaly understood the SIR model with all mathematical explanations you gave

@TomRocksMaths

4 жыл бұрын

That's great to hear :)

Cheers for this, needed it for my uni essay!

I am so glad to chance upon this video. Thank you.

@TomRocksMaths

4 жыл бұрын

Glad it was helpful Owen!

Thank you so much for making this video, it really helped my math modelling coursework, got 80+%🎉 ( I am in a UK uni so super happy with that ❤❤❤)

First of all i would like to say thank you for sharing your worthy information with us. As a mathematics student i think that,by familiarising the applications in mathematical field we tend more close to this field.Moreover,by explaining safety measures of this epidemic spread in a mathematical model is way more accessible. I would love to see more advanced models if that's something you are interested as well.Spread the math word and thank you once again. 🙏👏

@TomRocksMaths

4 жыл бұрын

Thanks Krishna - I discuss a more advanced model with spatial dependence here: kzread.info/dash/bejne/p4eAqNede6XUcqw.html

I'm so glad to find this video, thank you so much.

@TomRocksMaths

4 жыл бұрын

Glad it was helpful Lama!

Good one, I wish many people took up statistics as a subject which would make people understand the spread of a pandemic.

Very good explanation of the SIR model.

Outstanding explanations!! Thank you so much!!

@TomRocksMaths

3 жыл бұрын

You're very welcome Leonardo!

Thankyou tom❤️. fantabulous presentation. Loved it and understood almost everything clearly. And this is my project topic.

@TomRocksMaths

3 жыл бұрын

Glad it was helpful!

I would love to see some of the more advanced models

@pauvilimelisaceituno2893

4 жыл бұрын

Just a quick comment on some of the limitations of this model, particularly relating to the structure of interactions between people: The calculation of q requires having an average of people infected by patient. However, this assumes that we do have an average that converges to the expected value. This would be true if most people were to meet people regularly and randomly, but this is not necessarily the case. Humans interact in ways that often follow a heavy tailed distribution, meaning that few people have a very large number of connections, while most people have few. Similarly, people interact most days with a small sample of individuals and every now and then they have contact with a ton of individuals (ex: football match). In more mathematical terms: assume that the distribution of contacts per person follows a power law distribution (if we talk about the network of contacts this is often called scale-free networks), meaning that the probability of an individual having contact with k people on a given day is p(k) = k^-g where g> 0 and it is often between 2 and three. In that case, the moments of this distribution are mth moment = E[k^m]= integal [k^m p(k)] from k_min to infinity = (g-1)/(g-1-m) k_min ^m The problem with this is that for m=2, this gives us the variance, and it does not converge. In practical terms, this means that new samples would continuously change our average, hence prediction is difficult and needs further assumptions or "weaker" results. Naturally, if there are no large gatherings and very connected individuals do not touch a lot of people the distribution of contacts might shift to non-heavy tailed. Ref: R. Pastor-Satorras & A. Vespignani (2001). "Epidemic spreading in scale-free networks". Physical Review Letters. Other issues include: clustering (two of my friends have a high probability of being friends), or adding delays into the equations (since the number of recoveries does not depend directly on the number of infected people, but on the number of infected people days before). Ref: HW Hethcote, P van den Driessche - Journal of Mathematical Biology For further reading I would check the labs of Alessandro Vespignani or Victoria Colizza

@Lalit-yw2tb

4 жыл бұрын

@@pauvilimelisaceituno2893 thanks for the insight and the extra information.

@teresahanlon2205

4 жыл бұрын

try Corona Virus & Mathematical Modelling KZread. The Tutor Wizard Inc.

@chandelgaming8975

4 жыл бұрын

Please speak in hindi

@akhyarr

3 жыл бұрын

@@pauvilimelisaceituno2893 SIR is a basic model, with deterministic approach. We can develop (and make it more complicated 😁) by using stochastic solution, adding Expose compartment for delaying infection, etc..

In this video I learnt about the SIR model for diseases and that vertical stripes really accentuate hip movements.

@TomRocksMaths

4 жыл бұрын

Don't wear stripes on camera...

@OntologicalQuandry

4 жыл бұрын

@@TomRocksMaths no, just make sure to make the hip movements accentuate the maths being described. There were several variables that had much more impact for a little tick of the hips.

Oh man, I'm so happy I found this video! You're explanations were spot on! Here's a poem I wrote that you might enjoy: For Nietzsche a horse was the abyss that he gazed Cantor's Menge left his Geist behind For Frege a letter: set-foundation ablaze Russell's type too simple, unrefined Old Gödel starved from independence Turing tested apples, halting just the same Bourbaki brought austerity to their descendants But Coxeter grouped beauty with this formalist game Now, we know that S increased when Boltzmann hanged his brain and Noether's tumor was 'only' topological Grothendieck schemed so much and then he went insane Riemann and Ramanujan left before their prime But it's their heartiness and flux that let them pass the test of time Ehrhart taught high-school And Erdős was homeless In the end Euler went blind Little Andrew Weil beat the devil with a deal Weierstrass had demons too, concerning with the reals The foundations still shudder The Crisis, incomplete Brouwer's points don't fix or feel The shaking at our feet.

@TomRocksMaths

4 жыл бұрын

This is brilliant - thanks for sharing Kelly!

@Xeridanus

4 жыл бұрын

I don't get all of them but I get enough to realise just how brilliant this is.

Great video and explanation! I would love a video on one of the more advanced models if that's something you're interested in as well :)

such an worthy information..thanks👍🏼

Sir you just explained SIR model so very well, much learning when we go through various equations developed in model to scenario and everyone's perspective on it....i always found videos of yours explaining all the minute details.... keep up the good work :)

Very Good video! It is very clear even for me who do not understand english so well. Thank you so much!

@TomRocksMaths

4 жыл бұрын

Glad it was helpful Emilia!

This is fantastic. Thank you!

@TomRocksMaths

4 жыл бұрын

You're very welcome Tommy!

Thank you for this wonderful video.

Ty for making this video,if I have not seen this video I don’t even understand my parents since I don’t really understand the language I talk ty so much u explained it really well keep ur good work 😄

@TomRocksMaths

4 жыл бұрын

Awesome - thanks!

Wow. Thank you so much! I know your aim was to emphasize the importance of the precaution measures for COVID-19, but this video was very explanatory for my IB Mathematics SL Internal Assessment.

@TomRocksMaths

3 жыл бұрын

You're very welcome!

@alp4119

3 жыл бұрын

Hey, what do you investigate in your IA? I'm doing the same subject and I'm sure that I will use this topic but I couldnt figure out how..

@nahidameghji1510

3 жыл бұрын

@@alp4119 should I send you a sample IA I found on this same topic ?

@snigdhaadhikary9870

2 жыл бұрын

@@nahidameghji1510 hey even I wanted to use the SIR model for maths IA but I don’t really understand how. Could you please send me the sample IA?

I love your teaching way sir

@TomRocksMaths

3 жыл бұрын

Thanks Zohaib!

simple and wonderful explanation

@TomRocksMaths

4 жыл бұрын

Thanks!!

Excellent work! Very clearly explained. The wikipedia entry on the SIR model should include this video!

@TomRocksMaths

4 жыл бұрын

Thanks!! And glad you enjoyed it :)

Simply wonderful video! I graduated ten years ago with my bachelor's in math and I've ended up not really using it. (Partially because of a long bout with disability) BUT had I been taught about this connection to the medical field and mathematical modeling I may have continued my pursuit of mathematics further. I love math and medicine, but honestly hated differential equations because I had a terrible professor. Your real world application makes it very interesting even if completely understanding the details concerns me a bit more than the average person. Thanks for sharing!

@TomRocksMaths

4 жыл бұрын

Thanks Brittany, I'm glad you found it useful!

Thanks so much for the video. I have been asked to work on Covid modelling recently, but didn't really understand the meaning behind R0, you explain it very well, helps a lot! (Plus, you look very cool, not like the traditional math teacher at all ;) Thanks and keep up the good work!!

@TomRocksMaths

4 жыл бұрын

Awesome - thanks!!

Wow ...so clearly explained.👌 I will be doing my masters project ( most probably ) in modelling pandemics. Please keep making such videos.

@TomRocksMaths

3 жыл бұрын

There's a whole series on Disease Modelling here: kzread.info/head/PLMCRxGutHqfmBoC2YyFradH8NqpvbovMt

Thank u for the valuable information 😊

Hi Tom, Thanks for uploading this video

@TomRocksMaths

4 жыл бұрын

You're very welcome.

very informative, had a complete idea about SIR model related to any pandemic/epidemic

Thank you so much, it was awesome!

@TomRocksMaths

4 жыл бұрын

You're very welcome :)

I work in COVID testing and I find this very helpful.

@andrewgonzales1359

2 жыл бұрын

This will give me an understanding of where to allocate resources when this happens again. I’ve taken college level calculus and biology - thank you helping integrating the knowledge and disseminating it. I’m a former UCLA student and University of Minnesota - Twin Cities graduate.

@andrewgonzales1359

2 жыл бұрын

The last time in England was over a decade ago, and when I have spoken to Brits who have visited the United States, they love the NHS.

@andrewgonzales1359

2 жыл бұрын

Why am I learning about this year later and I’m the only person on my team who tried to learn this? I have no idea.

@andrewgonzales1359

2 жыл бұрын

Despite my experience with a chi-square analysis, I was not offered a position with an employer. This is what I have been learning in my spare time.

Is the sound of the chalkboard soothing to anyone else?

@TomRocksMaths

3 жыл бұрын

This.

@StNick119

3 жыл бұрын

Very much so. The gentle tap tap and scratch scratch, how pleasing.

Thanks from France... retired, coming from physics, I like when the universal mathematics language explains, especially from young people ... in physics we use spring, daspot, mass in "our" equation... the first simple non linear solution of such differential equation is the Weibull form, perhaps it could be inserted to see or smoothe the non symetric responses and anticipate that the queue is always wider... a special day as Christmas is only a "little" mass in the equation system etc... give a report of your explanations and it could be translated in other langage to young people every where

I got what i need for my project. Thank you soo much

@TomRocksMaths

3 жыл бұрын

You’re welcome 😊

Thank you this is so well explained

@TomRocksMaths

4 жыл бұрын

Glad it was helpful Elyn!

If you made video on intercept theorem thats grateful for me

The differential equation im interested in is dC/dB = RTC^2. Where dC/dB is the rate of colour change of the black coat next the the chalk board.

simple and clear good for beginners

@TomRocksMaths

4 жыл бұрын

Thanks Johnstone!

Awesome explanation! Thank you

@TomRocksMaths

3 жыл бұрын

Glad it was helpful Chris!

@LionsYouth

3 жыл бұрын

@@TomRocksMaths It really was! Rock on and happy holidays!

Oh my god. I understand!!! i finally understand! thank you.

@TomRocksMaths

3 жыл бұрын

Glad it helped Melvin :)

Unbelievable explanation that let's us think about Mathematical Modelling in our critical time and when we have no vaccine

@TomRocksMaths

4 жыл бұрын

Glad you enjoyed it Osama!

Your video is just awesome!!

I never paid attention to maths like this dude.

If I can make a suggestion, please keep the important equations, such as "q" written down, I had to go back to look it up every time. You have a whole left side of the board you're not using.

@TomRocksMaths

4 жыл бұрын

Noted - thanks for the feedback :)

@ggldmrd5583

4 жыл бұрын

@@TomRocksMaths Hi, i was programming the SIR model in python, but im stuck at the moment where i have to give values to the variable you call "r" and "a" into your video. What are the values for the covid19 and where/how to find them ? Im not looking for the exacts values cause i know it's impossible, but im looking for realistic values. On wikipédia i've seen that Ro = infection rate * average number of people met (per day) * number of days. Is it good to deduce that r = (Ro/people met)/number of days ? It looks logic but it gives stranges results. Results become more realistic when i consider that r = (Ro/population of the country)/number of days, but i don't understand why the population of the counrty would be in the equation. Also, for the value "a", do i have to consider that it equals to 1/number of days ? Or does is correspond to the recovered/infected ratio ? Nice video btw ;)

@TomRocksMaths

4 жыл бұрын

@@ggldmrd5583 these are very difficult values to obtain which is why I purposefully avoided including them in the video. I would suggest starting with the definitions I give in the video and then trying to interpret any available data that you can find to give approximate values. The value of a should be obtainable by looking at death/recovery rates for the disease. The value of r is more difficult but you could perhaps look up the same value for something like seasonal flu and increase it a little?

@ggldmrd5583

4 жыл бұрын

@@TomRocksMaths Thank you for your answer, about r im still in trouble, but your answer helped me for the other value. I also found that : www.lewuathe.com/covid-19-dynamics-with-sir-model.html which helped me for the other value. Indeed a = 1/time as i guessed. The source also mentions that r = Ro*a but it gives the results that i told you before, which is extremly low for a Ro (Ro = 0.0012 for Italia for exemple in this source, using this sort of low numbers i can do a good simulation, but using normal Ro values such as 3 or 4, it just doesn't work). Sorry for my english btw, it is not my primery langage.

@mclark23

4 жыл бұрын

@@ggldmrd5583 I think you need a variable R0. It's 2 or more at the start, but social distancing reduces it to maybe 1.4

Hey Tom, Thank you very much indeed for sharing this very important topics with the world. I ran through some the calculations and I came up with a slightly different result than yours @ 13:46 Let me break down my calculations: We have I+S-(1/q)lnS=I0+S0-(1/q)lnS0, rearranging it will give us: I=I0+S0-(1/q)lnS0-S+(1/q)lnS. Now, in order to calculate the IMax, we plugin S=1/q into the above equation. So we get the following: IMax=I0+S0-(1/q)lnS0-(1/q)+(1/q)ln(1/q) ==> IMax=I0+S0-(1/q)[lnS0+1-ln(1/q)] ==> IMax=I0+S0-(1/q)[1+ln(S0/q)] The only difference is in "ln(S0/q) vs ln(S0q)" I am not sure if I am right or not. But, if we think about it S0 is considerably a large fixed number, so if as q increases the product of qS0 increases accordingly, and so does the natural log. I would highly and greatly appreciate it if you could kindly comment and clarify this. Thanking you in advance and I look forward to hearing from you. Yours Sincerely, Koroush

@TomRocksMaths

4 жыл бұрын

Hi Koroush, I've gone through your working and there's a slight error in the last step when you manipulate the logs. We have -ln(1/q) which is equal to +ln(q) by the properties of logs. then we have ln(S0)+ln(q) which we can put together using the properties of logs to get ln(qS0). Hope that helps!

@koroushbozorgmehr3951

4 жыл бұрын

@@TomRocksMaths Thank you very much indeed Tom. I really appreciate the time you took to reply. Stay safe and healthy :)

@TomRocksMaths

4 жыл бұрын

@@koroushbozorgmehr3951 And you!

well explained. Job well done

Best explanation..😊

Great presentation my friend!

@TomRocksMaths

4 жыл бұрын

Thanks Nicolas!

Thank you so much

You're a Brit? How come I clearly get your words? I love it.

my math teacher assigned for us to watch over the “break” we have, we were suppose to take notes. Do you think that as an eighth grade class, we can understand this because I become lost many times?

@TomRocksMaths

4 жыл бұрын

It's certainly possible if you watch it several times and look up anything that you don't understand, but this is what I teach to my second year university students so don't worry at all about getting stuck!

@djnorm98

4 жыл бұрын

I found the explanation on Numberphile also very helpful. He sent us over here for more info.

@Xeridanus

4 жыл бұрын

Here is that video: kzread.info/dash/bejne/nWqirsh8kqTgl9I.html

@BCNeil

4 жыл бұрын

this would be pretty tough for your age....13? Instead of worrying about all the equations. You can still follow how changes in Q, change outcomes.

@lawrencejwinkler

4 жыл бұрын

If instead of differential equations, use difference equations. This uses discrete time steps but the equations are doable by hand. S(t+1) = S(t) - a I(t) S(t) I(t+1) = I(t) + a I(t) S(t) - b I(t) R(t+1) = R(t) + b I(t) So, no calculus, only algebra.

Right now I'm in 8th grade, and I have no idea what's going on but I still find everything quite intriguing. By the way, I came from Mike's channel :D Hopefully, these videos will help me in the future!

@TomRocksMaths

3 жыл бұрын

Awesome - and welcome :)

Best explanation ! Very good ! I have one question : the end of the outbreak is when I = 0, how do we know it will happend at finite time ?

@TomRocksMaths

4 жыл бұрын

Good point Pedro, and the answer is I guess we don't, but we can 'hope' that it is the case.

thank you, the 25min of the vid flew by

@TomRocksMaths

4 жыл бұрын

Awesome!!

Thanks for nice video😊

@TomRocksMaths

4 жыл бұрын

You're most welcome Aafiya 😊

We want more cool math people like you

Thank you for the video l am an aspiring mathematician interested in disease modelling

Conclusion: Please stay at home..

Hey Tom, this was a really detailed and great video! I really enjoyed it. What would you say is the PURPOSE of the SIR model? Like why model a disease using a SIR disease model in the first place?

@TomRocksMaths

3 жыл бұрын

Thanks - and really great question. We use this technique in mathematical modelling all of the time: start with the simplest possible model you can for a given situation, understand it, add an extra layer of complexity to make it more realistic, understand it, add another layer of complexity/realism, understand it, etc. Eventually the hope is that you get to a balance between something that you can understand/solve, AND is realistic enough to inform decision making. The SIR model was one of the first ever used to model disease spread and has now evolved into the incredibly complex and realistic computer-based models being used in the current pandemic.

Absolutely amazing video! However I found your conclusions a little bit unfounded. One of the basic hypotheses of this model is that the population perfectly mixing. If we fit this model to the real life data from countries where the infection is far gone, for exemple China, South Korea, or Italy, it's obvious that S(0) is way smaller, then the populations of these countries, even if we count with the undiagnosed cases. In fact, S(0) is rather the size of a fictive population in wich we can more or less assume perfect mixing. Speaking of South Korea S(0) is quiet low, around 8000 according my calculations based on fresh data. This shows us even more the importance of social distancing, because it's not just lowers the contact number, but also can isolate different groups of the society before the hole population get involved in the pandemic.

@curtiswfranks

4 жыл бұрын

My impression is that even a little bit of mixing causes the spread to basically match these predictions, just on their own timescales in each otherwise-isolated subpopulation. And, while we are at it, we should note that it is fractalic in nature: spread at the international level is similar to spread at the subnational regional level, which is similar to the spread at community level, which is similar to spread between households. So, any movement between 'populations' at any level in this heirarchy can kick off similar spreads throughout the entire hierarchy for the receiving population.

Is there a way to add a Brownian term to this? How would one go about it?

@TomRocksMaths

4 жыл бұрын

Yes, and it gets really really complicated really really quickly. I've purposefully started with the basic SIR model, but feel free to add to it!

@achrafouaddou1348

3 жыл бұрын

Tom Rocks Maths how we can do it ?

@ello7034

3 жыл бұрын

I have a question about the math. We already know the data on least likely to die and most likely to die. Why aren’t we using that data to build up a herd immunity that target specifically “those least likely to die” Protect the vulnerable and start building up a herd immunity using the data.(which is highly favourable for young healthy people)

@atrumluminarium

3 жыл бұрын

@@ello7034 I think the reason we don't is because it will be impossible from a social psychology stand-point. People objecting, breaking rules, thinking they know better, not really willing to intentionally infect themselves, etc. There's also the economic aspect where a sick person means a person not working. Hopefully with the vaccines, a similar effect will be achieved without all that hassle

Very clear, well explained,,, even I understood it.. so... you are a success ,,, jajaja

@TomRocksMaths

4 жыл бұрын

Awesome - thanks!

Very informative yet simply explained! You really helped me understand more details about the SIR model. I've actually done dynamic modelling before, but all my DEs were linear. I'm wondering if we can get the equations of S(t), I(t) and R(t) (most probably they would be exponentials). Is that possible?

@TomRocksMaths

4 жыл бұрын

The issue is that the equations are coupled (they all depend on each other) and so the clever tricks I use in the video (such as combining two of the equations to get one that we can integrate) are how we try to solve them - rather than solving explicitly like you say. We actually have an explicit equation for I and S together in Q2.

@asddsaasddsa1111

4 жыл бұрын

@@TomRocksMaths But this is not exactly the max infected at a time right? This is the max for I(S) function not I(t). Could you please help me to understand?

I wish you were my tutor in school

Wish you could show how to estimate R naught using that formula on a curve fitting for a particular data and time

Congratulations Tom, excellent tutorial. I have a question. You mention a function f (x) please What would be the independent variable x? I tell you this because everything you have indicated as f (x) contains only constants.

@TomRocksMaths

4 жыл бұрын

The variable is the contact ratio q. It is treated as a constant in the model, but we can affect the value in our daily lives by practicing measures such as social distancing. The purpose of treating it like a variable was to show what we can do to help to reduce the impact of the disease.

Just a question at 2:50, SIR model considers that the rate of transmition if S=10 and I=1000 is the same than if S=1000 and I=10 but from my intuition is more probable to get infected if there are just 10 healthys that have arround 1000 infecteds than if 1000 healthys have arround just 10 infecteds (the probability that a healthy get a contact with an infected in the second case is way to low)

@TomRocksMaths

3 жыл бұрын

I see your point, but remember that the S and I values also affect the derivative terms - so the dS/dt and dI/dt terms on the LHS. If you include this also then the equations agree with your explanation.

very very cool!!

How do you build in for the effectiveness of NPIs (Non Pharmaceutical Intervention)? The simplest way seems to be to adjust the infection rate ”r”. That feels like a bit of a fiddle as actually what's happening is the contact frequency between S and I are being reduced. What are sensible values for ”r” and ”a” for COVID? I am solving the differential equations numerically (I'm an engineer - we always find a simple ways to manipulate maths) and setting ”r” to get a doubling of cases every 3-4 days and then adjusting ”a” to show cases recovering or being removed in around 5-6 days following infection. That approximates to an R0 of 3.65. In reality recovery is taking 10-14 days so the model tends to overestimate R (Removed) relative to experience? I was going to set dR/dt=0 for the first 6 days of the simulation to try and get a better approximation of reality. A bit of an Engineer’s fudge once again but that should be ok I think? Analysing the results, I am perplexed about any forecast of relaxing NPIs in April, May, June or July. Reducing the rate of infection slows down the spread and manages hospital beds but actually prolongs the pandemic extending it far into the future (12-18 months?). The only way to stop it in its tracks seems to be absolute lockdown to get R0 below 1 and that requires lockdown well into the autumn with universal testing and rapid isolation of new cases and their immediate contacts thereafter.

@TomRocksMaths

4 жыл бұрын

Hi Don, thanks for your (very detailed!) response. You're right that reducing the rate of infection will indeed prolong the epidemic, but that is what we are aiming for at the moment as it buys us more time. More time means we have a chance of creating a vaccine, or just understanding more about what this virus is and how it works so that we can better implement methods to stop its spread. At the moment its all so new and unknown and the best thing we can do is to get time on our side.

@donharrold1375

4 жыл бұрын

Tom Rocks Maths Thanks for the reply. I've always loved mathematics and simulations in particular. It's often hard for non scientific people to appreciate that some of us actually use mathematics to solve real world problems and make our living doing so. Hardly a day has passed in my long career where some aspect of my mathematical education hasn't been invaluable. It's great that guys like yourself are trying communicate this type of stuff to give a wider audience a better appreciation of mathematical applications.

Nicely done.

@TomRocksMaths

3 жыл бұрын

Thanks Gerald!

Thank you, this is a great video even for people like me that have no knowledge on this type of subjects. Although there is just one thing I didn´t understand and would apreciate so much if someone could answer me. When finding the equation for the max number of infected people at certain time, after integrating, what is the reasoning behind making it equal to the initial conditions?

@TomRocksMaths

4 жыл бұрын

When you integrate an expression you have an 'integration constant' which is normally represented as +c. This is here because whenever you differentiate a constant term you will always get zero. To solve for the value of this constant you can insert the value at any time (as it's constant it cannot change) so we use the initial values (t=0) as we know what these are.

Good presentation- Zam from kuala lumpur

@TomRocksMaths

4 жыл бұрын

Thanks Zam!

Amazing!!!

@TomRocksMaths

3 жыл бұрын

Thanks Bobby!

Can you post excel version of this?

The graph of S end at 19:57 is quite different to yours when i plot it in my graphing calculator.

@TomRocksMaths

4 жыл бұрын

Hi Muhammad, you can actually see the exact curve I plotted at 23:01 in the top-left of the screen. If you copy the same equation into Desmos you should get the same results as me.

very nice

Hi Tom, why does s

@TomRocksMaths

3 жыл бұрын

We are replacing S with it's maximum value and so we know that I*(rS-a) < I*(rS(0)-a) but since the LHS is equal to the derivative we can get the equation you mention.

Hi Tom, I am attempting to use your model formulation for healthcare demand purposes... I am just wondering how you would go about finding a value for q based on (only) the government's social distancing tactics i.e. "If we reduce the contact by 50%, an infected person will pass it on to 1.25 people as opposed to 2.5? Or based on any other info out there for that matter?

@TomRocksMaths

4 жыл бұрын

Tricky question... the problem is the virus is so new that we just don't have enough data. Even something like 'seasonal flu' which has been around for hundreds of years isn't completely understood and requires some level of estimation of the parameter values. In practice, what we do is run the model for lots of different values of q to see which gives the best outcome, and then try to work out how to reach those particular values. The best suggestion I can give you is to try to find the same values for eg. seasonal flu and then increase them a little (as it seems COVID-19 spreads faster).

Do you have some PDE solver? I think SIR can be transferred into a reaction diffusion equation and that is a system to play with. Would like to but have to find some free solver. At least 1D for cylinder coordinates. Then you get a diffusion constant that you can play with, size of the area, influences of population densyties. etc. Nice bit about the max I !

@TomRocksMaths

4 жыл бұрын

There is some more information on how to this in the latest Numberphile video here: kzread.info/dash/bejne/nWqirsh8kqTgl9I.html

@TVWJ

4 жыл бұрын

It is not reaction plus diffusion. It is an autocatalytic reaction sequence. Pde solver: use Python.

Great video

Brilliant!

@TomRocksMaths

4 жыл бұрын

Glad you enjoyed it :)