Revisions to Solving Differential Equation System for HIV Treatment Model

added 9 characters in body

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edited Jan 17, 2021 at 13:10

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Structuring the script.

parms = {s -> 10, m1 -> 0.02, m2 -> 0.5, m3 -> 4.4, r -> 0.03, Tm -> 1500, k -> 0.000024, M -> 300, A -> 1, T0 -> 800, Ti0 -> 0.04, V0 -> 1.5};
x1 = T[t];
x2 = Ti[t];
x3 = V[t];
X = {x1, x2, x3};
Lambda = {la1[t], la2[t], la3[t]};
U = u[t];
f1 = s/(1 + x3) - m1 x1 + r x1 (1 - (x1 + x2)/Tm) - U k x1 x3;
f2 = U k x3 x1 - m2 x2;
f3 = M m2 x2 - m3 x3;
F = {f1, f2, f3};
L = A x1 - (1 - U)^2;
H = L + Lambda.F;
equ1 = Thread[D[X, t] == Grad[H, Lambda]];
equ2 = Thread[D[Lambda, t] == -Grad[H, X]];
equ3 = D[H, U] == 0;
solU = Solve[equ3, U][[1]];
equs = Join[equ1, equ2];
cinitsX = Thread[X == {T0, Ti0, V0}] /. {t -> 0};
cinitsLambda = Thread[Lambda == 0] /. {t -> 0};
cinits = Join[cinitsX, cinitsLambda];
vars = Join[X, Lambda];
DE = Join[equs, cinits] /. solU /. parms;
solDE = NDSolve[DE, vars, {t, 0, 10.01}];
Plot[Evaluate[XPlot[Evaluate[vars /. solDE], {t, 0, 10.01}]

Structuring the script.

parms = {s -> 10, m1 -> 0.02, m2 -> 0.5, m3 -> 4.4, r -> 0.03, Tm -> 1500, k -> 0.000024, M -> 300, A -> 1, T0 -> 800, Ti0 -> 0.04, V0 -> 1.5};
x1 = T[t];
x2 = Ti[t];
x3 = V[t];
X = {x1, x2, x3};
Lambda = {la1[t], la2[t], la3[t]};
U = u[t];
f1 = s/(1 + x3) - m1 x1 + r x1 (1 - (x1 + x2)/Tm) - U k x1 x3;
f2 = U k x3 x1 - m2 x2;
f3 = M m2 x2 - m3 x3;
F = {f1, f2, f3};
L = A x1 - (1 - U)^2;
H = L + Lambda.F;
equ1 = Thread[D[X, t] == Grad[H, Lambda]];
equ2 = Thread[D[Lambda, t] == -Grad[H, X]];
equ3 = D[H, U] == 0;
solU = Solve[equ3, U][[1]];
equs = Join[equ1, equ2];
cinitsX = Thread[X == {T0, Ti0, V0}] /. {t -> 0};
cinitsLambda = Thread[Lambda == 0] /. {t -> 0};
cinits = Join[cinitsX, cinitsLambda];
vars = Join[X, Lambda];
DE = Join[equs, cinits] /. solU /. parms;
solDE = NDSolve[DE, vars, {t, 0, 1}];
Plot[Evaluate[X /. solDE], {t, 0, 1}]

Structuring the script.

parms = {s -> 10, m1 -> 0.02, m2 -> 0.5, m3 -> 4.4, r -> 0.03, Tm -> 1500, k -> 0.000024, M -> 300, A -> 1, T0 -> 800, Ti0 -> 0.04, V0 -> 1.5};
x1 = T[t];
x2 = Ti[t];
x3 = V[t];
X = {x1, x2, x3};
Lambda = {la1[t], la2[t], la3[t]};
U = u[t];
f1 = s/(1 + x3) - m1 x1 + r x1 (1 - (x1 + x2)/Tm) - U k x1 x3;
f2 = U k x3 x1 - m2 x2;
f3 = M m2 x2 - m3 x3;
F = {f1, f2, f3};
L = A x1 - (1 - U)^2;
H = L + Lambda.F;
equ1 = Thread[D[X, t] == Grad[H, Lambda]];
equ2 = Thread[D[Lambda, t] == -Grad[H, X]];
equ3 = D[H, U] == 0;
solU = Solve[equ3, U][[1]];
equs = Join[equ1, equ2];
cinitsX = Thread[X == {T0, Ti0, V0}] /. {t -> 0};
cinitsLambda = Thread[Lambda == 0] /. {t -> 0};
cinits = Join[cinitsX, cinitsLambda];
vars = Join[X, Lambda];
DE = Join[equs, cinits] /. solU /. parms;
solDE = NDSolve[DE, vars, {t, 0, 0.01}];
Plot[Evaluate[vars /. solDE], {t, 0, 0.01}]

deleted 13 characters in body

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edited Jan 2, 2019 at 14:06

Cesareo

4k
8
12

Structuring the script.

parms = {s -> 10, m1 -> 0.02, m2 -> 0.5, m3 -> 4.4, r -> 0.03, Tm -> 1500, k -> 0.000024, M -> 300, A -> 1, T0 -> 800, Ti0 -> 0.04, V0 -> 1.5};
x1 = T[t];
x2 = Ti[t];
x3 = V[t];
cinitsXX = {x1 == T0, x2 == Ti0, x3 == V0} /. {t -> 0};
cinitsLambdaLambda = Thread[Lambda == 0] /. {tla1[t], ->la2[t], 0la3[t]};
U = u[t];
l1 = lambda1[t];
l2 = lambda2[t];
l3 = lambda3[t];
f1 = s/(1 + x3) - m1 x1 + r x1 (1 - (x1 + x2)/Tm) -k U k x1 x3;
f2 = U k x3 x1 - m2 x2;
f3 = M m2 x2 - m3 x3;
X = {x1, x2, x3};
F = {f1, f2, f3};
Lambda = {l1, l2, l3};
L = A x1 - (1 - U)^2;
H = L + Lambda.F;
equ1 = Thread[D[X, t] == Grad[H, Lambda]];
equ2 = Thread[D[Lambda, t] == -Grad[H, X]];
equ3 = D[H, U] == 0;
solU = Solve[equ3, U][[1]];
equs = Join[equ1, equ2];
cinitsX = Thread[X == {T0, Ti0, V0}] /. {t -> 0};
cinitsLambda = Thread[Lambda == 0] /. {t -> 0};
cinits = Join[cinitsX, cinitsLambda];
vars = Join[X, Lambda];
DE = Join[equs, cinits] /. solU /. parms;
solDE = NDSolve[DE, vars, {t, 0, 1}];
Plot[Evaluate[X /. solDE], {t, 0, 1}]

Structuring the script.

parms = {s -> 10, m1 -> 0.02, m2 -> 0.5, m3 -> 4.4, r -> 0.03, Tm -> 1500, k -> 0.000024, M -> 300, A -> 1, T0 -> 800, Ti0 -> 0.04, V0 -> 1.5};
x1 = T[t];
x2 = Ti[t];
x3 = V[t];
cinitsX = {x1 == T0, x2 == Ti0, x3 == V0} /. {t -> 0};
cinitsLambda = Thread[Lambda == 0] /. {t -> 0};
U = u[t];
l1 = lambda1[t];
l2 = lambda2[t];
l3 = lambda3[t];
f1 = s/(1 + x3) - m1 x1 + r x1 (1 - (x1 + x2)/Tm)-k U x1 x3;
f2 = U k x3 x1 - m2 x2;
f3 = M m2 x2 - m3 x3;
X = {x1, x2, x3};
F = {f1, f2, f3};
Lambda = {l1, l2, l3};
L = A x1 - (1 - U)^2;
H = L + Lambda.F;
equ1 = Thread[D[X, t] == Grad[H, Lambda]];
equ2 = Thread[D[Lambda, t] == -Grad[H, X]];
equ3 = D[H, U] == 0;
solU = Solve[equ3, U][[1]];
equs = Join[equ1, equ2];
cinits = Join[cinitsX, cinitsLambda];
vars = Join[X, Lambda];
DE = Join[equs, cinits] /. solU /. parms;
solDE = NDSolve[DE, vars, {t, 0, 1}]

Structuring the script.

parms = {s -> 10, m1 -> 0.02, m2 -> 0.5, m3 -> 4.4, r -> 0.03, Tm -> 1500, k -> 0.000024, M -> 300, A -> 1, T0 -> 800, Ti0 -> 0.04, V0 -> 1.5};
x1 = T[t];
x2 = Ti[t];
x3 = V[t];
X = {x1, x2, x3};
Lambda = {la1[t], la2[t], la3[t]};
U = u[t];
f1 = s/(1 + x3) - m1 x1 + r x1 (1 - (x1 + x2)/Tm) - U k x1 x3;
f2 = U k x3 x1 - m2 x2;
f3 = M m2 x2 - m3 x3;
F = {f1, f2, f3};
L = A x1 - (1 - U)^2;
H = L + Lambda.F;
equ1 = Thread[D[X, t] == Grad[H, Lambda]];
equ2 = Thread[D[Lambda, t] == -Grad[H, X]];
equ3 = D[H, U] == 0;
solU = Solve[equ3, U][[1]];
equs = Join[equ1, equ2];
cinitsX = Thread[X == {T0, Ti0, V0}] /. {t -> 0};
cinitsLambda = Thread[Lambda == 0] /. {t -> 0};
cinits = Join[cinitsX, cinitsLambda];
vars = Join[X, Lambda];
DE = Join[equs, cinits] /. solU /. parms;
solDE = NDSolve[DE, vars, {t, 0, 1}];
Plot[Evaluate[X /. solDE], {t, 0, 1}]

added 10 characters in body

Source Link

edited Jan 2, 2019 at 13:52

Cesareo

4k
8
12

Structuring the script.

parms = {s -> 10, m1 -> 0.02, m2 -> 0.5, m3 -> 4.4, r -> 0.03, Tm -> 1500, k -> 0.000024, M -> 300, A -> 1, T0 -> 800, Ti0 -> 0.04, V0 -> 1.5};
x1 = T[t];
x2 = Ti[t];
x3 = V[t];
cinitsX = {x1 == T0, x2 == Ti0, x3 == V0} /. {t -> 0};
cinitsLambda = Thread[Lambda == 0] /. {t -> 0};
U = u[t];
l1 = lambda1[t];
l2 = lambda2[t];
l3 = lambda3[t];
f1 = s/(1 + x3) - m1 x1 + r x1 (1 - (x1 + x2)/Tm);-k U x1 x3;
f2 = U k x3 x1 - m2 x2;
f3 = M m2 x2 - m3 x3;
X = {x1, x2, x3};
F = {f1, f2, f3};
Lambda = {l1, l2, l3};
L = A x1 - (1 - U)^2;
H = L + Lambda.F;
equ1 = Thread[D[X, t] == Grad[H, Lambda]];
equ2 = Thread[D[Lambda, t] == -Grad[H, X]];
equ3 = D[H, U] == 0;
solU = Solve[equ3, U][[1]];
equs = Join[equ1, equ2];
cinits = Join[cinitsX, cinitsLambda];
vars = Join[X, Lambda];
DE = Join[equs, cinits] /. solU /. parms;
solDE = NDSolve[DE, vars, {t, 0, 1}]

Structuring the script.

parms = {s -> 10, m1 -> 0.02, m2 -> 0.5, m3 -> 4.4, r -> 0.03, Tm -> 1500, k -> 0.000024, M -> 300, A -> 1, T0 -> 800, Ti0 -> 0.04, V0 -> 1.5};
x1 = T[t];
x2 = Ti[t];
x3 = V[t];
cinitsX = {x1 == T0, x2 == Ti0, x3 == V0} /. {t -> 0};
cinitsLambda = Thread[Lambda == 0] /. {t -> 0};
U = u[t];
l1 = lambda1[t];
l2 = lambda2[t];
l3 = lambda3[t];
f1 = s/(1 + x3) - m1 x1 + r x1 (1 - (x1 + x2)/Tm);
f2 = U k x3 x1 - m2 x2;
f3 = M m2 x2 - m3 x3;
X = {x1, x2, x3};
F = {f1, f2, f3};
Lambda = {l1, l2, l3};
L = A x1 - (1 - U)^2;
H = L + Lambda.F;
equ1 = Thread[D[X, t] == Grad[H, Lambda]];
equ2 = Thread[D[Lambda, t] == -Grad[H, X]];
equ3 = D[H, U] == 0;
solU = Solve[equ3, U][[1]];
equs = Join[equ1, equ2];
cinits = Join[cinitsX, cinitsLambda];
vars = Join[X, Lambda];
DE = Join[equs, cinits] /. solU /. parms;
solDE = NDSolve[DE, vars, {t, 0, 1}]

Structuring the script.

parms = {s -> 10, m1 -> 0.02, m2 -> 0.5, m3 -> 4.4, r -> 0.03, Tm -> 1500, k -> 0.000024, M -> 300, A -> 1, T0 -> 800, Ti0 -> 0.04, V0 -> 1.5};
x1 = T[t];
x2 = Ti[t];
x3 = V[t];
cinitsX = {x1 == T0, x2 == Ti0, x3 == V0} /. {t -> 0};
cinitsLambda = Thread[Lambda == 0] /. {t -> 0};
U = u[t];
l1 = lambda1[t];
l2 = lambda2[t];
l3 = lambda3[t];
f1 = s/(1 + x3) - m1 x1 + r x1 (1 - (x1 + x2)/Tm)-k U x1 x3;
f2 = U k x3 x1 - m2 x2;
f3 = M m2 x2 - m3 x3;
X = {x1, x2, x3};
F = {f1, f2, f3};
Lambda = {l1, l2, l3};
L = A x1 - (1 - U)^2;
H = L + Lambda.F;
equ1 = Thread[D[X, t] == Grad[H, Lambda]];
equ2 = Thread[D[Lambda, t] == -Grad[H, X]];
equ3 = D[H, U] == 0;
solU = Solve[equ3, U][[1]];
equs = Join[equ1, equ2];
cinits = Join[cinitsX, cinitsLambda];
vars = Join[X, Lambda];
DE = Join[equs, cinits] /. solU /. parms;
solDE = NDSolve[DE, vars, {t, 0, 1}]

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edited Jan 2, 2019 at 13:46

Cesareo

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created Jan 2, 2019 at 13:07

Cesareo

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