Langmuir model with QSS
In this worksheet I am working on the identifiability of the parameters of a model of antibody binding.
usefull lists and sets
In this worksheet we shall obtain results and look at the case where the inlet concentration, is known
or alternately unknown
set up equations
Set up B equations
Set up y equations
Set up C equations
(2.1)
obtain y and derivatives multinomial quotient
(2.1.1)
(2.1.1)
(2.1.2)
notably we can't re assign the function
eliminate B1
(2.1.3)
(2.1.4)
(2.1.5)
take a derivative
(2.1.6)
(2.1.7)
deal with quotients and phases
at I_i=0
at I_i=C_t*d_i
however there are two cases, either C_T is known or not, so we create two numhats and two
denhats
known:
unknown:
look at products
we know that if
at I_i=0
at I_i=C_t*d_i
known
(2.3.2.1)
unknown
look at coefficients
at I_i=0
7
(2.4.1.1)
at I_i=C_t*d_i
known
unknown
find solutions
konwn
(2.5.1)
unknown
(2.5.2)
(2.5.2)