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- เผยแพร่เมื่อ 15 ก.ย. 2024
- Explains the approaches for the mathematical modelling of the spread of infectious diseases such as Coronavirus (COVD-19, SARS-CoV-2). This video explains the classic compartmental models in the epidemics literature such as SIR, SIS, SEIR etc. It also explains key concepts such was reproduction number, final size equation, and the key theorems that are implied by these concepts.
Amazing!!! I was thinking how much these models relate to the stochastics used in Finance and here you put up this legendary piece!
thanks @Brian Staroselsky! Infinitesimals are micro-creatures at the end of the day!!
@@quantpie Do you think based on the various regional data a good stochastician using these models would be able to fit reasonably good estimations of vital parameters if they were to continue calibrating ? Or would one need to employ a stronger statistical mechanics approach with some mean field theory approximations? I figured in reality the models that best approximate and are best for these situations are far more complex then SEIR, and take into account dynamical systems theory.
If the data is reliable, then the simple models should provide a good approximation of the average behaviour. For example, the reproduction number (R0) can be estimated using the daily increase in infections plus a metric called generation time /serial interval, which requires case level data. There are also a few publicly available data sources for estimating the other parameters.
Now retuning to the R0, the problem is that infection counts is largely incorrect when the disease is unfolding as not everyone get tested. And the data required for generation time is even more limited (please see this article: academic.oup.com/aje/article/180/9/865/2739204). The SARS estimates were way off - the estimates suggested reproduction number in the range of 2-4, when in the end it only infected just 8000 people.
But then the mean field theory extension of these models (which we are aiming to cover at some point) have similar data issues. So the main challenge is data! or shall we say reliability of the data. We need clever data collection/cleansing methods!
@@quantpie thanks for the detailed response, super stoked and looking forward to the further installments. Do you think because the data is the biggest issue at this time, that conventional time series techniques from finance like arima based models or even more complicated ideas like Markov switching models and wavelet and time frequency analysis models be of any use for this sort of forecasting / epidemiology modelling? If the data was accurate and we had better testing methods and sampling as a result, I am curious if we would see some multifractal / multiscale behavior and if the process is extremely noisy and non ergodic.
thanks Brian! Conventional time series models will be too susceptible to the data issues, may have a chance when the dust has settled - they look beautiful when fitted to historical data! However, the actuarial type survival analysis/truncation are useful tools in parameters estimation as they allow one to remove biases. Experimental analysis, that you implied in the sense of sampling methods, is very useful in data collection, but this is tricky business, though public authorities do collect detailed data.
This is an amazing video! Please, it would be great if you cover Stochastic Models as well! I will really use them and try to simulate it in my stochastic integrators! Thanks a lot!
thanks @Ramiro Vignolo! Coming up shortly!
Delighted to see such a good video!!! Stay safe!
thanks @Cong Bao!! Stay safe too!
Do you think that the stochastic S(E)IR model is more realistic? I would love to see a video on that
Indeed, especially when combined with segmentation of the compartments (e.g., strata by vulnerability groups), or simple network/graphs. Have uploaded the stochastic version!
quantpie Thank you very much. Didn‘t expect the video to be uploaded that quickly! :) keep up the very great work!
thanks!
I need modeling of covid 19 do you help me this is my title of search???
@@mimihd5252 sure! it is a great topic, very much looking forward to it! Plz use the email address that you can find in the contact section, and let us know how we can help!
Is there a way to distinguish between pseudo-random and true random numbers?
Thanks for the question @roulette-lab! If you have a pseudo-random numbers generator/sequence, then a number of tests are available, ranging from simple visual to very advanced analysis of patterns -please see this NIST document: nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication800-22r1a.pdf.
By true random numbers, may I check if you have some natural process/experimental conditions in mind, or do you mean the properties that a good random number generator is expected to possess?
Great! I learnt so much from your video. Thank you sir.
thank you!!
Loved the video but would it be possible to site any sources?
What are exact solutions in PDEs?
These refer to solutions that can be written using 'some formula/expression'!
Excellent, no one was able to explain better than you
Thanks! We do try so glad to hear you found it informative!
This is a pure mathematician's approach to the classic SIR model. Instead of numerical integration [ which is easier to understand and to implement, and into which it's a simple matter to introduce stochastic methods ] the presenter chooses to derive formal definite integrals. This assumes that the functions in the model are integrable, which in my own view is a dubious assumption. At the end, it's an elegant piece of work but if you're interested in possible end results, you're still going to be dependent on the constants of proportionality. In other words this is an exercise in pure math, not of any greater value than simpler methods if you're interested in real-world dynamics.
As with most things, the devil is in the details. At this time hard and reliable data are next to impossible to find because of generally poor understanding of how to collect meaningful data, the expense and practical difficulty of doing so even if you did know what you were doing, the lack of consistency in applying the various protocols in testing, false positives and false negatives, not to mention politically motivated falsehoods and human frailty in general. It gets even worse when it is realized that the virus affects different people in different ways; so ultimately accurate predictions are doomed because of the heteroscedasticity which this implies.
Sad to say no amount of good mathematics, pure or applied, can cut through this jungle. I suppose with many of us trapped in lockdown it can be fun to spend time trying to find some rational approach as a vehicle for understanding.
Excellent observation Harold. You're 100% correct. There are far too many variables and unknowns in pandemics in general. It's very easy to do simple maths and come up with "zillions will die' And of course that plonker the so call "professor" Ferguson of Knotty Ash University otherwise referred to as "Imperial College" proved that time and again over a ten year period with his "swine flu" "BSE" and other "predictions". The bloke in charge of him should give him the boot immediately and send him the bloody bill for all the damage he's caused us all !
He won't be so randy when he's bankrupt and no bird will ever go near him cos he's skint and working collecting the bins in Scottie Road
On a more serious note. He was lauded as the one eye'd man in the "land of the blind" A specialist that had a computer model written in Egyptian Hieroglyphics that no other person had ever seen and of course it was never published. That tells you and me that the people who appointed him and paid his don't know even the first thing about pandemics and how to prepare for them. So Ferguson is NOT the only one who needs to get the boot. His bosses should also get shown the door.
Personally I'd integrate any useful formula into a spreadsheet that could be downloaded by any member of the public and then checked by anyone of us who cares to do so
As I'm sure you all know already it only takes one person to infect two others and then they infect four others
Follow that through and using a simple calculator, you'll see that having done that 21 times you are over a million infected people, 22 times and it's doubled again to two million
I guess if you do it about 50 times you've got the whole of the UK's 60 million all infected.
That's a basic mathematical model, BUT our common sense tells us that won't happen, or if it does the whole country is not going to die of the virus. They might die with numerous other problems, typically various cancers, diabetes and numerous other chronic illnesses and the virus was simply too much for their frail body to cope with
So, then we all now know from previous flu pandemics that about 3% or less will die, so that means 97% of us won't die of the virus
So what did they do with infectious diseases 2,000 years ago. Lepers were put into a "leper colony" to protect the healthy. Well that's what they did in the movie "Ben Hur". But they had obvious symptoms of leprosy and therefore could be identified.
So what do we do with people in modern times in the 21st century. We isolate people with infectious disease in isolation wards. Ebola and TB are typical examples. But this virus is more difficult to deal with because it betrays no symptoms in the early stages of infection but is able to transmit to others during that period
That one fact makes it much more difficult to deal with
But going back to previous pandemics the history shows the death rate is usually about 3% or less
ONLY when it's know for sure that the death rate will rise much higher, say 6 or 7% should drastic measure be taken and although 6% is possible, it's not very likely
Therefore with all this new information we can only hope that the next time we have a pandemic we have people in charge who actually know their job inside out. The likes of the pillock in the WHO Tedros should also be given the bullet for aiding and abetting the Chinese Communist Party by spreading their lies and bullshit and then we have to "have a word with China"
I can tell you one thing for sure and that is "If there is no very nasty and severe consequences for The Chinese Communist Party then they will do the same thing again and again"
Kind regards to you all and hopefully one of you will produce that spreadsheet I mentioned - Chris in Thailand
thanks Harold for the very constructive feedback. Yes the purpose of this video was to introduce the basic modelling framework, hoping to inspire some interest. We aim to cover more advanced models- many of these models, as you mentioned, present considerable analytical challenges, and even numerical treatment is hard in most cases, though there are some nice stochastic simulation algorithms that are relatively accessible. So far we have covered the models that formed the basis of the BBC contagion, and the metapopulation models - both of these models have been considered by SAGE, so no model is perfect but these are the types of models that inform decisions. Our aim is not to sell models but rather to explain the maths and hopefully inspire some interest in the maths behind the headlines. The data challenges that one encounter here have inspired a lot of statistical research, and if there were to be interest, we would love to cover the statistical topics. Many thanks!
The nut of this explanation, or any other mathematical modeling of SARS-COV2 spread is the population has already been saturated. Depending on when one starts the clock on patient zero, the planet has already reached saturation, which means there is no person living within a society with contact with other regions who hasn't been contacted by SARS-COV2 as of September 2021. Herd immunity has already been attained.
Can you do some videos on the Coupla concept? :D Maybe some examples? Awesome video.
thanks, added to the list 👍
@@quantpie
okie! We never finished the Vasicek portfolio loss playlist, so going to get back to the series once we have finished the work-in-progress videos!
I wonder if the virus can amalgamate and become a super virus
please start discord server please