@kflo I don't know if this is right but it's more reasonable. I solved most of this by hand and programmed it. There could be MANY places where I messed up.
I did the following:
1) Took the curve for the single dose.
2) Reverse engineered a differential equation that it would satisfy (specifically a non-homogeneous linear third order differential equation with a constant as the non-homogeneous term)
3) Added a series of shifted delta functions to the right hand side (i.e. the non-homogeneous term)
4) Resolved the differential equation with the new appended non-homogeneous term, with laplace transforms and whatnot.
Got the following. Again many places where I could have messed up so I'll have to trudge through it again. That said my results are more reasonable in the sense that we have substantially longer detection windows and smaller amounts.
I could figure out how to solve numerically but that could get troublesome with delta functions and whatnot.
The delta functions are supposed to represent new doses.
@kflo why you leaving me hanging brah? I also noticed that now some people think I’M A PAID SHILL.
Shit I wish I was. You know how baller it would be to be paid big bucks to save athletes from suspensions? Far fetched but it would be awesome.