Langmuir model with transport
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
B equations
y equations
C equations
eliminate B1
substitute the above into some equations
create an equation to later get rid of C_ij
or B_2
obtain y and derivatives multinomial
Create further derivatives
second derivative
create a list of things to substitute into them
because we can no longer simplify y2
third derivative
the following is horrible
deal with quotients
at I_i=0
at I_i=C_T
C_T known
C_T unknown
look at products
we know that if
at I_i=0
at I_i=C_T*d_i
known
unknown
look at coefficients
at I_i=0
at I_i=C_t*d_i
known C_T
unknown C_T
Create sets of equations for known and unknown C_T
for the known case
for the unknown case
solve
Solve the system of equations from the coefficients where C_T is known (this command causes
problems it may be better to look at the solution for unknown
and make appropriate
substitutions)
Solve the system of equations from the coefficients whilst I_i=C_T, where C_T is unknown
(8.1)