
Bilirubin2

seed_ := 65$

NUMBER OF EQUATIONS$

n_ := 5$

VARIABLES VECTOR$

b_ := {x1,
x2,
x3,
x4,
u1,
y1}$

UNKNOWN PARAMETER(S) VECTOR$

b1_ := {k01,
k12,
k13,
k14,
k21,
k31,
k41}$

RANKING AMONG THE VARIABLES$

bb_ := {x1,
x2,
df(x1,t),
df(x2,t),
df(x1,t,2),
df(x2,t,2),
df(x1,t,3),
df(x2,t,3),
df(x1,t,4),
df(x2,t,4),
x3,
x4,
u1,
y1,
df(x3,t),
df(x4,t),
df(u1,t),
df(y1,t)}$

NUMBER OF INPUT(S)$

nu_ := 1$

NUMBER OF OUTPUT(S)$

ny_ := 1$

NUMBER OF STATE(S) $

nx_ := 4$

MODEL EQUATION(S)$

c_ := {df(x1,t)= - (k41*x1 - u1 + k31*x1 + k21*x1 - k14*x4 - k13*x3 - k12*x2) - k01*x1,
df(x2,t)= - k12*x2 + k21*x1,
df(x3,t)= - k13*x3 + k31*x1,
df(x4,t)= - k14*x4 + k41*x1,
y1=x1}$

CHARACTERISTIC SET$

aa_(1) := df(x2,t) - x1*k21 + x2*k12$

aa_(2) := df(x1,t) - u1 + x1*(k01 + k21 + k31 + k41) - x2*k12 - x3*k13 - x4*k14$

aa_(3) :=  - x1 + y1$

aa_(4) := df(x3,t) - x1*k31 + x3*k13$

aa_(5) := df(x4,t) - x1*k41 + x4*k14$

MODEL NOT ALGEBRAICALLY OBSERVABLE$

RANDOMLY CHOSEN NUMERICAL PARAMETER(S) VECTOR$

b2_ := {k01=63,k12=41,k13=38,k14=35,k21=32,k31=23,k41=8}$

EXHAUSTIVE SUMMARY $

flist_ := { - k21 + 32,k12 - 41}$

MODEL PARAMETER SOLUTION(S)$

 G_:=GROESOLVE(FLIST_,B1_) $

g_ := {{k12=41,k21=32}}$

MODEL NON IDENTIFIABLE$

IDENTIFIABILITY WITH THE KNOWN INITIAL CONDITION(S)$

bi_ := {x1,x2,u1,u1,y1,y1}$

aai_(2) := df(x1,t) - u1 + x1*(k01 + k21 + k31 + k41) - x2*k12 - x3*k13 - x4*k14$

aai_(3) :=  - x1 + y1$

ic1_ := {}$

BBBI_ INCLUDES THE BB_ ENTRIES CALCULATED AT T=0$

bbbi_ := {df(x2,t,2)=x2d20,
df(x1,t,2)=x1d20,
df(x2,t)=x2d10,
df(x1,t)=x1d10,
x2=x20,
x1=x10,
u1=u1_0,
y1=y1_0}$

UNKNOWN PARAMETER(S) VECTOR$

b1i_ := {k01,
k12,
k13,
k14,
k21,
k31,
k41,
u1_0,
y1_0}$

EXHAUSTIVE SUMMARY EVALUATED AT TIME T=0 $

bbi_ := {x2d10,x20}$

flisty_ := { - 32*x10 + 41*x20 + x2d10, - 38*x3 - 35*x4 + 126*x10 + x1d10 - 41*x20 - 10}$

 GY_:=GROESOLVE(FLISTY_,BBI_)$

gy_ := {{x20=( - 38*x3 - 35*x4 + 126*x10 + x1d10 - 10)/41,
x2d10=38*x3 + 35*x4 - 94*x10 - x1d10 + 10}}$

RANDOMLY CHOSEN NUMERICAL PARAMETER(S ) VECTOR$

b2i_ := {k01=63,k12=41,k13=38,k14=35,k21=32,k31=23,k41=8,u1_0=10,y1_0=49}$

EXHAUSTIVE SUMMARY$

flist1i_ := { - k21 + 32,
k12 - 41,
(x3*(38*k12 - 41*k13) + x4*(35*k12 - 41*k14) + 41*k01*x10 - 126*k12*x10 - k12*x1d10 + 10*k12 + 41*k21*x10 + 41*k31*x10 +
 41*k41*x10 - 41*u1_0 + 41*x1d10)/41,
 - x10 + y1_0}$

GI_=GROESOLVE(FLIST1I_,B1I_)  $

gi_ := {{y1_0=x10,
k01=(k13*x3 + k14*x4 - k31*x10 - k41*x10 + u1_0 + 94*x10 - 38*x3 - 35*x4 - 10)/x10,
k12=41,
k21=32}}$

MODEL NON IDENTIFIABLE$
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