Mathematical Biology. 15: SIR Model

UCI Math 113B: Intro to Mathematical Modeling in Biology (Fall 2014)
Lec 15. Intro to Mathematical Modeling in Biology: SIR Model
View the complete course: ocw.uci.edu/courses/math_113b_...
Instructor: German A. Enciso, Ph.D.
Textbook: Mathematical Models in Biology by Leah Edelstein-Keshet, SIAM, 2005
License: Creative Commons CC-BY-SA
Terms of Use: ocw.uci.edu/info
More courses at ocw.uci.edu
Description: UCI Math 113B is intended for both mathematics and biology undergrads with a basic mathematics background, and it consists of an introduction to modeling biological problems using continuous ODE methods (rather than discrete methods as used in 113A). We describe the basic qualitative behavior of dynamical systems in the context of a simple population model. As time allows, we will then discuss other types of models such as chemical reactions inside the cell, or excitable systems leading to oscillations and neuronal signals. The necessary linear algebra is also discussed to avoid including additional requirements for this course.
Recorded on February 12, 2014
Required attribution: Enciso, German A. Math 113B (UCI OpenCourseWare: University of California, Irvine), ocw.uci.edu/courses/math_113b_.... [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License. (creativecommons.org/licenses/b...)

[@lamaabdullah1937]

The most amazing lectures that I have seen in mathematical biology, seen many times without boring.

[@DaughterOfChrist1997]

Best explanation so far

[@mananamin9210]

Very well explained and much more intuitive 👍

[@dearmichiko2912]

Awesome, I admire the topic, and of course the way lecturere delivered it.. This will be one of my reference as I'm gonna teach math-bio although this isn't really my field of study. And while listening to the epidemic part, I just couldn't stand it, as I imagine how the students perceived when the lecturer said about, say, 'when some new viruses exist from the middle of nowhere, we should wonder whether this will be epidemic or not'. If I sat in that class, I would think: let's hope there's no such thing like epidemic for the whole earth. And yet, here we are: human now facing, battling the large epidemic of covid 19. Let's pray for better future, for this disease vanish quickly and nicely, and everybody get well, then do better life. And I hope all of the students (and the lecturer of course), in this video, blessed by God- safe and sound, feeling the gratitude of the opportunity they had: attending inspirational class few years ago

[@umarbashir7196]

i find the lecture very interesting

[@CarlosRomeroFilosofia]

COVID-19 brought me here. 😜

[@hajiralidakheel6306]

me too :/

[@jairjuliocc]

The same, i am trying to implement this model for data of my country

[@tshepoSamuel]

My final year design project 😂😂

[@s.prakash7869]

Awesome Lecture

[@osuf3581]

I think it's a good first approximation but it is not the case that viral load plays no part in transmission; along with enabling modeling of host response

[@jayprice6376]

Glenn - pretty simple response from me - Go Irish!!! You stayed non-political and yet delivered a very potent explanation of truth!!! Can you explain why different states show different curves? Based on your explanation it doesn’t appear like the virus should be so different across state lines!!

[@jorgeananjofloresgalindo4479]

how could I identify the values for beta and gamma?

[@triton62674]

fascinating

[@wimthiels638]

thx helped a lot

[@leonardocabrera9253]

Biology and Mathematics the best combination to fight off any desease.

[@crustyoldfart]

Try and convince the politicians of that.

[@ishfaqahmad8495]

I found the lectures and watched it. it is very interesting

[@crustyoldfart]

How about an SIR model with stochastic inputs, based on available medical and demographic data, with the aim of replecating observed [ real world ] results of the spread of COVID 19, country by country.

[@ishfaqahmad8495]

@@crustyoldfart Professor I think SEIR model country bases with demographic effects especially immigration emigration for the model of COVID 19 will be more interesting because in my country majority of cases occurs due to exposed immigrants. But I am wondering social behavior is also the factor for this COVID 19. What is your kind suggestions for this.

[@crustyoldfart]

@@ishfaqahmad8495 Thank you for the question. I should explain that for some reason my comment [ which was intended for another commentator who was wondering about a thesis topic based on the basic SIR model. ] somehow got placed as a reply to your comment instead. If I understand your project it involves both immigration and emigration during the period of time you are modelling. This would seem to violate the zero-sum assumption which is implicit in the simple SIR model. I would think that it would be possible to model a non-zero-sum model with a stochastic input to the basic SIR, and carry out a numerical integration. In fact it should be possible to carry out numerical integration on pretty well any stochastic arrangement we care to postulate. But as the saying goes " the proof of the pudding is in the eating ". Thus ultimately the value of the model as it is conceived will depend on how well it replicated real events. As a practical matter this is probably difficult to do during the time the epidemic is playing out, but not impossible, insofar as if past behaviour is closely modelled, there is a possibility of this model being a successful predictor of future behaviour. The open question is to what degree lawmakers care to use the modelling process. The Climate Change question is a case in point. Experience shows that lawmakers will pick the model they need to justify what they have already decided to do. Best wishes for your future success.

[@ishfaqahmad8495]

@@crustyoldfart Thank you very much respectable professor

[@arwahsapi]

This subject makes more sense in time like this

[@anjanbhattacharjeesir]

Thank you so much for

[@IsomerSoma]

Writing my Seminar Work about SIR stability analysis. Wish me luck. Hallo gab.

[@zenaal-khatib6903]

Hi, I am struggling in figuring out how to solve the SIR model

[@zotac1018]

you are not alone

[@crustyoldfart]

It depends what you consider to be a solution. An easy way to proceed is to assume values for the two rate constants - he used beta and v - which respectively define the rate of infection and the rate of recovery. You then carry out a step by step numerical integration. If you have a lot of patience you can do this using a pencil and paper and a calculator. If you have even more patience you can do without the calculator. Just remember to make N*beta/v > 1

[@jellyfishbones0]

I did a model in excel using approximate DE's, one row per day, its works fine. just brute force it bruh. do you even excel ?

[@khadijakhadija-mn3yn]

hey.. i m just starting my thesis in this field... please suggest me a topic

[@Ghulammurtaza-bf9yh]

Please anyone send me this book.

[@abezadama6261]

Wow

[@kaliisakaita5831]

Intelligent and handsome teacher😂

[@cassandrah580]

does this model not account for births/deaths?

[@thomaslangemarktrojahn8113]

Nope, not in the basic form - which is to say, the simplest form of the model - which is the SIR. There are various ways to expand the model to account for all kinds of different dynamics, as for example when one includes birth and death. The wikipedia article is really good, check that out.

[@davidsweeney111]

I love mathematical splogology!

[@pyeiphyolin6793]

22:44 an example of a disease within SIRS framework: COVID-19.

[@vivianadipietro6942]

[@ahmedalanbagi1416]

Man those boards are micro small

[@ThodorisHadoulis]

I hope the guy caughing in the audience doesnt have #covid19!

[@franklehouillier8865]

It would have been hard to have had it in 2014.