[R-sig-dyn-mod] Diffusion-reaction model out of polymer cylinder

[Edgardo Rivera]

Hi dynamic modeling group,

I am trying to model a diffusion-reaction transport process based on a paper by 
[Fu et.al](https://link.springer.com/article/10.1007%2Fs10439-011-0336-z)
but fail to demonstrate mass is conserved for the system as a test of my
implementation.

The paper simulates the release of a small molecule out of the top and bottom 
faces of a thin cylindrical polymer with no wall transport. Within the polymer
cylinder, the molecule drug can either diffuse (LIGAND) or it can react
reversibly  with an immobile host (COMPLEX). The resulting system of ode is
solved with the method of lines. Since cylinders are symmetricals the system of 
equations is simplified to have no release from the bottom face and transport 
occurs only through the top face.

The model is used to simulate the cumulative release process of a drug out of 
the polymer cylinder into liquid media. The paper by Fu implements the 
solution in matlab using ode15s and I would like to translate this approach to R 
using deSolve. I wanted to ask for your help answering the following questions:

(1) Does the code in the repo seems like a reasonable implementation of the model
in deSolve?
(2) Do you have any ideas why I may be experiencing a lack of mass conservation 
in the system? Wrong code, wrong implementation or other reason?

Reproducible example location
[github repo](https://github.com/eriveradelgado/ODE_Practice/blob/master/05_Reproducible-Example.Rmd)
[session info](https://github.com/eriveradelgado/ODE_Practice/blob/master/2019-01-24_session-info.Rmd)
---
Any general suggestions or feedback are always appreciated. I wanted to be as 
clear as possible so ended up with a verbose post. In the future, I can reduce 
the length if that's preferred by the list members and/or moderator. Thank you.


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