
HIV

seed_ := 65$

NUMBER OF EQUATIONS$

n_ := 6$

VARIABLES VECTOR$

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

UNKNOWN PARAMETER(S) VECTOR$

b1_ := {b,
c,
d,
q1,
q2,
k1,
k2,
w1,
w2}$

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)= - (d*x1 - u1) - b*x1*x4,
df(x2,t)= - (k1 + w1)*x2 + b*q1*x1*x4,
df(x3,t)=k1*x2 - w2*x3 + b*q2*x1*x4,
df(x4,t)= - c*x4 + k2*x3,
y1=x1,
y2=x4}$

CHARACTERISTIC SET$

aa_(1) := df(x2,t)*q2 - df(x3,t)*q1 + x2*(k1*q1 + k1*q2 + q2*w1) - x3*q1*w2$

aa_(2) :=  - df(x1,t)*df(x2,t) - df(x1,t)*x2*(k1 + w1) + df(x2,t,2)*x1 + df(x2,t)*x1*(c + k1 + w1) - x1**2*x3*b*k2*q1 + 
x1*x2*c*(k1 + w1)$

aa_(3) := df(x2,t) - x1*x4*b*q1 + x2*(k1 + w1)$

aa_(4) :=  - df(x1,t)*q1 - df(x2,t) + u1*q1 - x1*d*q1 - x2*(k1 + w1)$

aa_(5) :=  - x1 + y1$

aa_(6) := df(x2,t) - x1*y2*b*q1 + x2*(k1 + w1)$

MODEL ALGEBRAICALLY OBSERVABLE$

NORMALIZED  INPUT /OUTPUT RELATION(S) $

aan_(1) := (df(x2,t)*q2 - df(x3,t)*q1 + x2*(k1*q1 + k1*q2 + q2*w1) - x3*q1*w2)/q2$

aan_(2) :=  - df(x1,t)*df(x2,t) - df(x1,t)*x2*(k1 + w1) + df(x2,t,2)*x1 + df(x2,t)*x1*(c + k1 + w1) - x1**2*x3*b*k2*q1 +
 x1*x2*c*(k1 + w1)$

RANDOMLY CHOSEN NUMERICAL PARAMETER(S) VECTOR$

b2_ := {b=63,c=41,d=38,q1=35,q2=32,k1=23,k2=8,w1=10,w2=49}$

EXHAUSTIVE SUMMARY $

flist_ := { - b*k2*q1 + 17640,
( - 32*q1*w2 + 1715*q2)/(32*q2),
 - k1 - w1 + 33,
( - 32*q1 + 35*q2)/(32*q2),
c*k1 + c*w1 - 1353,
c + k1 + w1 - 74,
(32*k1*q1 + 32*k1*q2 + 32*q2*w1 - 1861*q2)/(32*q2)}$

MODEL PARAMETER SOLUTION(S)$

 G_:=GROESOLVE(FLIST_,B1_) $

g_ := {{b=16128/(k2*q2),w2=49,c=41,q1=(35*q2)/32,w1=10,k1=23}}$

MODEL NON IDENTIFIABLE$
Elapsed time for HIV: 1.2110235 seconds
