Mathematical Biology. 03: Nondimensionalization

UCI Math 113B: Intro to Mathematical Modeling in Biology (Fall 2014)
Lec 03. Intro to Mathematical Modeling in Biology: Nondimensionalization
Instructor: German A. Enciso, Ph.D.

Textbook: Mathematical Models in Biology by Leah Edelstein-Keshet, SIAM, 2005

License: Creative Commons CC-BY-SA

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 January 10, 2014

[MagiaEreba]

Thanks so much for this! After scouring the net, I finally stumbled upon this video. I finally understand nondimensionalization. Thank you!

[mmorenozambrano]

so, at the end you get rid off the units of everything... this might be a silly question, but now that we ended up with this dimensionless model, and if I want to estimate the alphas from experimental data, I just would have to use experimental data measured in the units that were considered before the non dimensionlization (does that word exist?, btw) and then run any numerical solver to estimate those? am I right?

[WalkAbout]

41:33 took differential equations his freshman year

[bigboateng]

If you only care about the Nondimensionalization part then skip to 17:00

[ngoziibe]

Good concept. Am enjoying this. Please.. Can we model the spread of malaria

[alexpb]

I´m a biologist, I wish I had math class in my undergraduate but was not possible. so these class is being amazing to me. Thank Prof Enciso!!!

[learnmathematics]

the lecture solved my a lot of problems in nondimensionalization thanks a lot

[miaositing]

Thank you very much for this video. It’s very helpful.

I’ve got one suggestion. In the process of choosing Ñ, C tilde and tau, instead of only emphasizing they should be chosen to simplify the model, they should have the same dimension as N, C and tau respectively such that the new variables are dimensionless. Correct me if I’m wrong.

[atharvashinde]

I think the book is Mathematical models in biology by Leah Edelstein-Keshet

[panda]

 Lecturer explains everything clearly and in detail.Thank you very much.

[cynthiaramirez]

OMG you're amazing!!!! I get this now :) Thank you!

[natureiscool]

This analysis is incorrect, he should have incorporated the flow term in the time derivative of the bacteria concentration into the time derivative of the food concentration
that is, there should be (K(c)N-F/V*N) in the dC/dt equation instead of just K(c)N
'because C' = K(c)N

[mariamorsillo]

I am confused @37:23 why would he talk about N hat if there is no N hat there I think he is referring to N*