
BIOMD03

seed_ := 65$

NUMBER OF EQUATIONS$

n_ := 6$

VARIABLES VECTOR$

b_ := {x1,
x2,
x3,
y1,
y2,
y3}$

UNKNOWN PARAMETER(S) VECTOR$

b1_ := {p1,
p2,
p3,
p4,
p5,
p6,
p7,
p8,
p9,
p10,
p11,
p12,
p13}$

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),
y1,
y2,
y3,
df(y1,t),
df(y2,t),
df(y3,t)}$

NUMBER OF INPUT(S)$

nu_ := 0$

NUMBER OF OUTPUT(S)$

ny_ := 3$

NUMBER OF STATE(S) $

nx_ := 3$

MODEL EQUATION(S)$

c_ := {df(x1,t)=( - ((p7 + x1)*p5 + p6*x3)*x1 + (p7 + x1)*p4)/(p7 + x1),
df(x2,t)=( - (p3 + x1)**(( - 1)/(x2 - 1 - p8))*(p10 + x2)*p1*x1 - (p3 + x1)**(( - x2)/(x2 - 1 - p8))*p9*x2)/((p3 + x1)**
(( - x2)/(x2 - 1 - p8))*(p10 + x2)),
df(x3,t)=( - ((p13 - p2*x2)*x3 - p12*p2*x2)*(x3 - 1) + p11*p13*x3)/((x3 - 1 - p11)*(p12 + x3)),
y1=x1,
y2=x2,
y3=x3}$

CHARACTERISTIC SET$

aa_(1) := df(x1,t)*x1 + df(x1,t)*p7 + x1**2*p5 + x1*x3*p6 + x1*( - p4 + p5*p7) - p4*p7$

aa_(2) := (x1 + p3)**(x2/( - x2 + p8 + 1))*df(x2,t)*x2 + (x1 + p3)**(x2/( - x2 + p8 + 1))*df(x2,t)*p10 + (x1 + p3)**(1/(
 - x2 + p8 + 1))*x1*x2*p1 + (x1 + p3)**(1/( - x2 + p8 + 1))*x1*p1*p10 + (x1 + p3)**(x2/( - x2 + p8 + 1))*x2*p9$

aa_(3) :=  - df(x3,t)*x3**2 + df(x3,t)*x3*(p11 - p12 + 1) + df(x3,t)*p12*(p11 + 1) + x2*x3**2*p2 + x2*x3*p2*(p12 - 1) - 
x2*p12*p2 - x3**2*p13 + x3*p13*(p11 + 1)$

aa_(4) :=  - x1 + y1$

aa_(5) :=  - x2 + y2$

aa_(6) :=  - x3 + y3$

MODEL ALGEBRAICALLY OBSERVABLE$

NORMALIZED  INPUT /OUTPUT RELATION(S) $

aan_(1) := df(x1,t)*x1 + df(x1,t)*p7 + x1**2*p5 + x1*x3*p6 + x1*( - p4 + p5*p7) - p4*p7$

aan_(2) := ((x1 + p3)**(x2/( - x2 + p8 + 1))*df(x2,t)*x2 + (x1 + p3)**(x2/( - x2 + p8 + 1))*df(x2,t)*p10 + (x1 + p3)**(1
/( - x2 + p8 + 1))*x1*x2*p1 + (x1 + p3)**(1/( - x2 + p8 + 1))*x1*p1*p10 + (x1 + p3)**(x2/( - x2 + p8 + 1))*x2*p9)/(p3 + 
1)**(1/p8)$

aan_(3) :=  - df(x3,t)*x3**2 + df(x3,t)*x3*(p11 - p12 + 1) + df(x3,t)*p12*(p11 + 1) + x2*x3**2*p2 + x2*x3*p2*(p12 - 1) -
 x2*p12*p2 - x3**2*p13 + x3*p13*(p11 + 1)$

RANDOMLY CHOSEN NUMERICAL PARAMETER(S) VECTOR$

b2_ := {p1=63,
p2=41,
p3=38,
p4=35,
p5=32,
p6=23,
p7=8,
p8=10,
p9=49,
p10=25,
p11=22,
p12=45,
p13=12}$

EXHAUSTIVE SUMMARY $

flist_ := {p7 - 8,
p5 - 32,
p6 - 23,
 - p4*p7 + 280,
p10 - 25,
p1 - 63,
p1*p10 - 1575,
p9 - 49,
p2 - 41,
 - p12*p2 + 1845,
 - p13 + 12,
 - p4 + p5*p7 - 221,
p12*p2 - p2 - 1804,
p11 - p12 + 23,
p11*p12 + p12 - 1035,
p11*p13 + p13 - 276}$

MODEL PARAMETER SOLUTION(S)$

 G_:=GROESOLVE(FLIST_,B1_) $

g_ := {{p6=23,
p9=49,
p1=63,
p10=25,
p4=35,
p5=32,
p11=22,
p13=12,
p7=8,
p2=41,
p12=45}}$

MODEL NON IDENTIFIABLE$

IDENTIFIABILITY WITH THE KNOWN INITIAL CONDITION(S)$

BBBI_ INCLUDES THE BB_ ENTRIES CALCULATED AT T=0$

bbbi_ := {df(x3,t,3)=x3d30,
df(x2,t,3)=x2d30,
df(x1,t,3)=x1d30,
df(x3,t,2)=x3d20,
df(x2,t,2)=x2d20,
df(x1,t,2)=x1d20,
df(x3,t)=x3d10,
df(x2,t)=x2d10,
df(x1,t)=x1d10,
x3=x30,
x2=x20,
x1=x10,
x1=1/100,
x2=1/100,
x3=1/100,
y1=y1_0,
y2=y2_0,
y3=y3_0}$

UNKNOWN PARAMETER(S) VECTOR$

b1i_ := {p1,
p2,
p3,
p4,
p5,
p6,
p7,
p8,
p9,
p10,
p11,
p12,
p13,
y1_0,
y2_0,
y3_0}$

EXHAUSTIVE SUMMARY EVALUATED AT TIME T=0 $

bbi_ := {x3d10,
x2d10,
x1d10,
x30,
x20,
x10}$

flisty_ := {32*x10**2 + x10*x1d10 + 23*x10*x30 + 221*x10 + 8*x1d10 - 280,
(63*(x10 + 38)**(10/(x20 - 11))*x10**2*x20 + 1575*(x10 + 38)**(10/(x20 - 11))*x10**2 + 2394*(x10 + 38)**(10/(x20 - 11))*
x10*x20 + 59850*(x10 + 38)**(10/(x20 - 11))*x10 + x20*x2d10 + 49*x20 + 25*x2d10)/((x10 + 38)**(11/(x20 - 11))*(x10 + 38)
),
41*x20*x30**2 + 1804*x20*x30 - 1845*x20 - x30**2*x3d10 - 12*x30**2 - 22*x30*x3d10 + 276*x30 + 1035*x3d10,
 - x10 + 50,
 - x20 + 20,
 - x30 + 46}$

 GY_:=GROESOLVE(FLISTY_,BBI_)$

gy_ := {{x2d10=(28*( - 7840800*2**(1/3)*11**(1/9) - 7))/9,
x1d10=( - 71835)/29,
x3d10=3345204/2093,
x20=20,
x10=50,
x30=46}}$

RANDOMLY CHOSEN NUMERICAL PARAMETER(S ) VECTOR$

b2i_ := {p1=63,
p2=41,
p3=38,
p4=35,
p5=32,
p6=23,
p7=8,
p8=10,
p9=49,
p10=25,
p11=22,
p12=45,
p13=12,
y1_0=50,
y2_0=20,
y3_0=46}$

EXHAUSTIVE SUMMARY$

flist1i_ := {p7 - 8,
p5 - 32,
p6 - 23,
 - p4*p7 + 280,
p10 - 25,
p1 - 63,
p1*p10 - 1575,
p9 - 49,
p2 - 41,
 - p12*p2 + 1845,
 - p13 + 12,
 - p4 + p5*p7 - 221,
p12*p2 - p2 - 1804,
p11 - p12 + 23,
p11*p12 + p12 - 1035,
p11*p13 + p13 - 276,
(2*(p3 + 50)**(1/(p8 - 19))*( - 109771200*(p3 + 50)**(19/(p8 - 19))*2**(1/3)*11**(1/9)*p10 - 2195424000*(p3 + 50)**(19/(
p8 - 19))*2**(1/3)*11**(1/9) - 98*(p3 + 50)**(19/(p8 - 19))*p10 + 90*(p3 + 50)**(19/(p8 - 19))*p9 - 1960*(p3 + 50)**(19/
(p8 - 19)) + 225*p1*p10 + 4500*p1))/9,
(2*(1672602*p11*p12 + 48139*p11*p13 + 76939692*p11 + 941850*p12*p2 - 75267090*p12 - 2166255*p13 + 43325100*p2 - 
3462286140))/2093,
y1_0 - 50,
y2_0 - 20,
y3_0 - 46}$

GI_=GROESOLVE(FLIST1I_,B1I_)  $

gi_ := {}$

MODEL NON IDENTIFIABLE$
Elapsed time for BIOMD03: 1.0199403 seconds
