A DAE model example

The DAE model is similar to an ODE model, except for that the expression should be written to only include a right-hand-side (rhs). If we have e.q. an algebraic equation ALG like: ALG = k1 - 5, it should be rewritten as 0 = k1 - 5 - ALG. Optionally, it could also likely be rewritten as 0 = ALG - k1 + 5.

Due to the way the compilation to C-code is implemented, algebraic states will end up after the ODE-states. Thus, it is advised to put the algebraic states and initial conditions at the end of STATES heading.

Also note that it is typically necessary to pass along an extra option to the Simulation function, with the calcic flag set to True:

options = {'calcic': True}

An example of a DAE model is given below.

########## NAME
Insulin
########## METADATA
time_unit = s
########## MACROS
########## STATES
d/dt(INS) = PRODUCTION - UPTAKE - CLEARANCE
0 = INS - ALGSTATE
INS(0) = 5
ALGSTATE(0) = 5
########## PARAMETERS 
k1 = 1
k2 = 1
########## VARIABLES
CLEARANCE = k2*INS
########## FUNCTIONS
########## EVENTS
########## OUTPUTS
INSULIN = INS
########## INPUTS
UPTAKE = INS_UPTAKE
PRODUCTION = ACTIVITY_IN @ 0
########## FEATURES
INS = INS # Mol
ALGSTATE = ALGSTATE