
Bilirubin1

seed_ := 65$

NUMBER OF EQUATIONS$

n_ := 6$

VARIABLES VECTOR$

b_ := {x1,
x2,
x3,
x4,
u1,
y1,
y2}$

UNKNOWN PARAMETER(S) VECTOR$

b1_ := {k03,
k04,
k13,
k24,
k31,
k42,
k43}$

RANKING AMONG THE VARIABLES$

bb_ := {x1,
x2,
x3,
df(x1,t),
df(x2,t),
df(x3,t),
df(x1,t,2),
df(x2,t,2),
df(x3,t,2),
df(x1,t,3),
df(x2,t,3),
df(x3,t,3),
df(x1,t,4),
df(x2,t,4),
df(x3,t,4),
x4,
u1,
y1,
y2,
df(x4,t),
df(u1,t),
df(y1,t),
df(y2,t)}$

NUMBER OF INPUT(S)$

nu_ := 1$

NUMBER OF OUTPUT(S)$

ny_ := 2$

NUMBER OF STATE(S) $

nx_ := 4$

MODEL EQUATION(S)$

c_ := {df(x1,t)= - (k31*x1 - u1) + k13*x3,
df(x2,t)=k24*x4 - k42*x2,
df(x3,t)=k31*x1 - k43*x3 - k13*x3 - k03*x3,
df(x4,t)=k42*x2 + k43*x3 - k24*x4 - k04*x4,
y1=x1,
y2=x2}$

CHARACTERISTIC SET$

aa_(1) := df(x3,t) - x1*k31 + x3*(k03 + k13 + k43)$

aa_(2) := df(x2,t,2) + df(x2,t)*(k04 + k24 + k42) + x2*k04*k42 - x3*k24*k43$

aa_(3) := df(x2,t) + x2*k42 - x4*k24$

aa_(4) := df(x1,t) - u1 + x1*k31 - x3*k13$

aa_(5) :=  - x1 + y1$

aa_(6) :=  - x2 + y2$

MODEL ALGEBRAICALLY OBSERVABLE$

RANDOMLY CHOSEN NUMERICAL PARAMETER(S) VECTOR$

b2_ := {k03=63,k04=41,k13=38,k24=35,k31=32,k42=23,k43=8}$

EXHAUSTIVE SUMMARY $

flist_ := { - k31 + 32,
k04*k42 - 943,
 - k24*k43 + 280,
k03 + k13 + k43 - 109,
k04 + k24 + k42 - 99}$

MODEL PARAMETER SOLUTION(S)$

 G_:=GROESOLVE(FLIST_,B1_) $

g_ := {{k03= - k13 - k43 + 109,
k31=32,
k04=(sqrt(6029*k43**2 - 55440*k43 + 78400) + 99*k43 - 280)/(2*k43),
k24=280/k43,
k42=( - sqrt(6029*k43**2 - 55440*k43 + 78400) + 99*k43 - 280)/(2*k43)},
{k03= - k13 - k43 + 109,
k31=32,
k04=( - sqrt(6029*k43**2 - 55440*k43 + 78400) + 99*k43 - 280)/(2*k43),
k24=280/k43,
k42=(sqrt(6029*k43**2 - 55440*k43 + 78400) + 99*k43 - 280)/(2*k43)}}$

MODEL NON IDENTIFIABLE$
Elapsed time for Bilirubin1: 1.011501 seconds
