KevCaz
commented
6 years ago What a great idea!! 👍 👍 and I want to be involved, let me in, please, please!!!
It's a vast topic though and from what I am reading you won't actually cover everything (I mean of course you won't and you don't have to but we may refine the title according to the topics you are covering, e.g.: a taste of differential equations in R).
Regarding the structure I have a couple of suggestions.
First, I think that the question:
Why mathematical modeling?
you've righteously asked should be the topic of first post of the series. You may first ask why model? (google have proven me that we won't be the first asking this question! http://jasss.soc.surrey.ac.uk/11/4/12.html) than briefly mention what king of model exist and then detail the scope of the collection of posts and especially if theses posts will have a math focus or an in silico focus or both (everything would suit me well).
In post 2 you could give a simple example of ODE (and give some context about ODE) and I think it would be a wonderful idea to create a function to visualize the ODE (I've already done that). I really think it would be worth spending some time discussing about the mathematical object we are dealing with before solving it.
Post 3 may discuss about the numerical methods available to solve ODE and you may provide home-made code lines that implement them (e.g. Euler, Runge-Kutta).
In post 4 you could detail how to solve ODE with DeSolve and rootSolve (and detail what they are actually using). I now use odeintr and I can show how to use it. We may carry some benchmarking out.
In post 5, you could spend some time about what to do with the results or even deal with sensitivity analysis.
I think that would enough for now, we can plan solving other kind of equations latter. Dealing with diffusion can easily be 3 other posts and dealing with master equations 3 others!! Let's start with a reasonable number of posts. Again the above suggestions are by no means guide lines and only reflect my sole opinion. Anyway you'll do, this it will be a nice collection of posts to show how to solve differential equations in R or whatever.
A side note we can also give some mathematica / sage command line to solve equations.
Azenor
Hi gang, @willvieira and I thought of doing a series of post on mathematical modelling inspired from a workshop we are doing at the uni on the book "A Biologist's guide to Mathematical Modeling in Ecology and Evolution" from Otto and Day. We wrote a short description of the posts here. Let us know what you think about the idea, the structure and if you'd like to participate! :)
Mathematical Modeling in Ecology with R
Post 1
Why mathematical modeling?
Advantages and disadvantages.
Chapter 1: introduction
Chapter 2: how to construct a model?
Example of a simple model in R. (Two species mutualism interaction model?)
Primer post ?!
Linearization
Post 2
Equilibria and stability analysis of the model introduced previously (Chapter 5).
Package
DeSolveandrootSolveode(),runsteady(),multiroot()and other functionsjacobian.full()...Post 3
Graphical representation of stability analysis
Phase plan: Illustration of eigenvectors (associated to eigenvalues). (Van der Pol oscillator?)
Post 4
General solutions and linear algebra
Post 5
Probabilistic models: add stochasticity to our toy model and analyze it
Post 6
Analyzing continuous stochastic models: Diffusion in time and space