How likely is coronavirus (COVID-19) eradicated? [PART II]

Part 2 of a series of videos 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 explore how we can extract the extinction probability (probability that coronavirus will eventually get eradicated) from the BGW process using the cobwebbing technique. Although it is not a rigorous approach, it is a very nice visual way to see what's happening. We then, not too surprisingly, come up with the concept of basic reproduction number, a concept that is seen in both the BGW model and the SIR model.

This video will involve concepts like distribution, independence, expected value, generating function, and the cobwebbing techniques to visualise iteration processes and so on, but a basic understanding of the concept of probabilities will be good, and basic understanding on differentiation (definition as slope of a function, power rule and linearity of the differential operator) will be required.

The next video on the limitations / improvement and the historical context of the BGW process should be released in a couple of days, because they are already done.

REFERENCES / SOURCES (which I will explain in much more detail in later videos that I promised, but if you are impatient, you can read these):

(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]

Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:

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

SUBSCRIBE and see you in the next video!

If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I will probably reveal how I did it in a potential subscriber milestone, so do subscribe!

#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.

Social media:

For my contact email, check my About page on a PC.

See you next time!

[mathemaniac]

UP NEXT: "Limitations of mathematical models; historical context of BGW process [PART III]" will be released on Monday. Like and share this video and subscribe!

If you want this channel to be more geared towards your math levels, do fill in the following Google form:
The more people who fill in the form, the better I could gauge the math levels of my audience.

[ASOUE]

Holy cow, I came from your dream video and I must say I am so impressed. You are on par with 3b1b (not to detract from your individuality, but your style leads me to believe you draw heavy inspiration from him and will understand this is a compliment). I cannot believe you don’t have many subs. You’re my new math fix. You’ll be seeing me around

[laviekolchinsky]

Yes, it's all in the reproductive number! The derivation in the end is very nice, and it's also a good model for some period where the SIR model doesn't help such as when there is no inflection point for the model to deal with. This type of model is what people talked about when discussing "flattening the curve", since the exponential growth means little people can infect many, varying on an individual basis. However, the average reproduction number of the people has to be minimised. This is also why large gathering of people are banned. Thanks for the video and the number of uploads is awesome.