There's a whole area for this - pharmacokinetics. See e.g. https://en.wikipedia.org/wiki/Biological_half-life#Rate_equa... for examples of e.g. first order models (exponential elimination rate, etc.) It has to do with protein binding dynamics among other factors I have no idea about. Remember that you are dealing with biological systems.

Some of these processes to do with elimination and clearance are very much non-linear and are modelled with diff equations. https://en.wikipedia.org/wiki/Physiologically_based_pharmaco...