
Thyroid2

seed_ := 65$

NUMBER OF EQUATIONS$

n_ := 4$

VARIABLES VECTOR$

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

UNKNOWN PARAMETER(S) VECTOR$

b1_ := {k02,
k03,
k12,
k13,
k21,
k31}$

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),
x3,
u1,
y1,
df(x3,t),
df(u1,t),
df(y1,t)}$

NUMBER OF INPUT(S)$

nu_ := 1$

NUMBER OF OUTPUT(S)$

ny_ := 1$

NUMBER OF STATE(S) $

nx_ := 3$

MODEL EQUATION(S)$

c_ := {df(x1,t)= - (k31*x1 - u1 + k21*x1 - k13*x3) + k12*x2,
df(x2,t)= - (k12*x2 - k21*x1) - k02*x2,
df(x3,t)= - (k13*x3 - k31*x1) - k03*x3,
y1=x1/v1}$

CHARACTERISTIC SET$

aa_(1) := df(x2,t) - x1*k21 + x2*(k02 + k12)$

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

aa_(3) :=  - x1 + y1*v1$

aa_(4) := df(x3,t) - x1*k31 + x3*(k03 + k13)$

MODEL NOT ALGEBRAICALLY OBSERVABLE$

RANDOMLY CHOSEN NUMERICAL PARAMETER(S) VECTOR$

b2_ := {k02=63,k03=41,k12=38,k13=35,k21=32,k31=23}$

EXHAUSTIVE SUMMARY $

flist_ := { - k21 + 32,k02 + k12 - 101}$

MODEL PARAMETER SOLUTION(S)$

 G_:=GROESOLVE(FLIST_,B1_) $

g_ := {{k02= - k12 + 101,k21=32}}$

MODEL NON IDENTIFIABLE$

IDENTIFIABILITY WITH THE KNOWN INITIAL CONDITION(S)$

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

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

aai_(3) :=  - x1 + y1*v1$

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_ := {k02,
k03,
k12,
k13,
k21,
k31,
u1_0,
y1_0}$

EXHAUSTIVE SUMMARY EVALUATED AT TIME T=0 $

bbi_ := {x2d10,x20}$

flisty_ := { - 32*x10 + 101*x20 + x2d10, - 35*x3 + 55*x10 + x1d10 - 38*x20 - 8}$

 GY_:=GROESOLVE(FLISTY_,BBI_)$

gy_ := {{x20=( - 35*x3 + 55*x10 + x1d10 - 8)/38,x2d10=(3535*x3 - 4339*x10 - 101*x1d10 + 808)/38}}$

RANDOMLY CHOSEN NUMERICAL PARAMETER(S ) VECTOR$

b2i_ := {k02=63,k03=41,k12=38,k13=35,k21=32,k31=23,u1_0=8,y1_0=10}$

EXHAUSTIVE SUMMARY$

flist1i_ := { - k21 + 32,
k02 + k12 - 101,
(x3*(35*k12 - 38*k13) - 55*k12*x10 - k12*x1d10 + 8*k12 + 38*k21*x10 + 38*k31*x10 - 38*u1_0 + 38*x1d10)/38,
v1*y1_0 - x10}$

GI_=GROESOLVE(FLIST1I_,B1I_)  $

gi_ := {{y1_0=x10/v1,
k02= - k12 + 101,
k13=( - 55*k12*x10 - k12*x1d10 + 35*k12*x3 + 8*k12 + 38*k31*x10 - 38*u1_0 + 1216*x10 + 38*x1d10)/(38*x3),
k21=32}}$

MODEL NON IDENTIFIABLE$
Elapsed time for Thyroid2: 1.0088593 seconds
