Limitations of mathematical models; historical context of BGW process [PART III]

Part 3 of a series on a stochastic process approach to model the spread of coronavirus (COVID-19) as opposed to the compartmental deterministic SIR model. This model is generally known as branching process, but this video only focuses on the simplest type, called Bienaymé-Galton-Watson (BGW) process. This video will especially be on the inevitable limitations on the BGW process model, to illustrate the limitations of any mathematical model in general. There can be problems in applicability and difficulty in interpreting data from the predictions of the model, but we can always strive to make the model more realistic. But the cost would be more complicated mathematics, and higher computing power necessary.

The historical context of the Bienaymé-Galton-Watson (BGW) process will be also discussed in this video, and it is actually a bit more interesting than usual. It is not just that the three mathematicians got together and studied this process.

I currently don't have a solid plan for my future videos, but feel free to comment below about the topics that I can cover in a future video!

REFERENCES / SOURCES:

(1) Branching Processes: Their Role in Epidemiology [basis / limitations / improvement of the model]

(2) Branching Processes Since 1873 [historical context of the Bienaymé-Galton-Watson process]

(3) The Genealogy of Genealogy Branching Processes before (and after) 1873 [historical context of the Bienaymé-Galton-Watson process]

(4) The Educational Times (March 1873) [Galton's original famous Problem 4001; historical context of the Bienaymé-Galton-Watson process]

(5) The Educational Times (August 1873) [Watson's (brief) answer to the Problem 4001; historical context of the Bienaymé-Galton-Watson process]

(6) On the probability of extinction of families [Watson's paper / more detailed albeit partially incorrect answer to the Problem 4001; historical context of the Bienaymé-Galton-Watson process]

(8) Guardian [KFC party breaking recent lockdown in Melbourne]:

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If you want to know more interesting Mathematics, stay tuned for the next video!

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#mathemaniac #math #coronavirus #COVID_19 #SIRmodel #statistics #probability #epidemic #pandemic

Stay safe everyone! Please do wear a mask to protect ourselves, and stay at home as much as possible. We will get through this together.

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See you next time!

[mathemaniac]

I hope that I haven't butchered the Bienyamé pronunciation, because I don't speak French, and pronunciations are difficult to research. Many apologies for that.

This is the end of the trilogy of videos! If you enjoyed these, like and share this video, and subscribe! If you find some other limitations / improvements of the BGW process model, do leave a comment to initiate further discussions!

so that I can guage your maths levels to produce better videos.

[hubertorhant]

So clean and competant work. The big picture is easy to understand. On the historical part, ''funny'' is the subject matter motivated the research.

[abbasmehdi]

Ooo ! Thats what makes complete .
Quality content😍 . Now more confidentally , I can say that - rather than basic operations - there lies true maths in daily life
I felt very bad 200 guys watch but didn't reacted so much .
They will realise soon .
What about game theory from next ? Just suggesting

[Henriiyy]

So isn't the BGW process much more limited than the SIR model, even when having a size-dependent offspring distribution? Because the SIR model actually makes a prediction about the evolution of R, while it would have to be assumed for a corrected BGW process.

[subscriberwithoutconten]

Pls make a video on godel incompleteness theorem