[R] Tools to transform/expand expressions (e.g. for ODE models)?

[Leonard Mada]

Dear R-Users,


I would like to generate automatically the mathematical expressions for 
some more advanced SIR-models.


The models should be specified using a simpler syntax. The R parser can 
parse various types of formulas/expressions. And I am wondering if there 
are tools available to help with the expansion and transformation of the 
intermediary expressions to the exact ODE expressions.


Example:

# Stratification: Y = Young adults; O = Old;

model = "S ~ Y + O; I ~ .; H ~ .; S %*% I -> I; S %*% H -> I;
    I -> H + R + D; H -> R + D; V ~ .; (time >= t0) & S^0 -> V;"
model = strsplit(model, ";")[[1]];

for(sM in model) {
   eq = parse(text = sM); # works nicely up to here
   # beyond: tools would be helpful;
}


### Model Description

1.) Stratification:
- stratified compartment: S ~ Y + O; [Young & Old]
- stratified compartment inheriting strata from parent compartment: I ~ .;

2.) Evolution
- simple: H -> R + D;
   => dH[Y] = - H[Y] * (k[Hy, Ry] + k[Hy, Dy]);
   # Note: R & D are not stratified;
   => dR = H[Y] * k[Hy, Ry] + H[O] * k[Ho, Ro];
- simple interaction: S * I -> I;
   => dS[Y] = - k[Sy, Iy] * S[Y] * I[Y];
- full interaction: S %*% I -> I;
   => dS[Y] = - S[Y] * (k[Sy, Iy] * I[y] + k[Sy, Io] * I[O]);
   # Note: all components of I interact (as if it was not-stratified);


1.) Tools

I would like to avoid to reinvent the wheel. Maybe there are some useful 
tools.

The current model description syntax is not final/fixed: changes are 
possible.

The model definition used by package dMod is useful for chemical 
reactions, but is not quit what I have in mind:

https://cran.r-project.org/web/packages/dMod/vignettes/dMod.html


2.) Explicit Models on Github

Various models with explicit mathematical formulas are available on 
GitHub and will be part of a BSc thesis:

https://github.com/BicaAnamaria/EpidemicSimulator


3.) Model Description

The description of the model syntax is available as an issue on GitHub 
as well:

https://github.com/BicaAnamaria/EpidemicSimulator/issues/35


Although I did not find tools that could help to easily convert the 
expressions, I might have missed them. There might be such tools - even 
outside the scope of ODE expressions - and I would be grateful for any 
hints.


Sincerely,


Leonard