I want to write maple code of the following algorithm with

the following parameters and initial values please help me.

T₀ = 5.5556 × 10⁷ cells, I₀ = 1.1111 × 10⁷ cells, V₀ = 6.3096 × 10⁹ copies/ml,

A_1=A2=1,

c = 0.67, h = 1, d = 3.7877 × 10⁻³, δ = 3.259d,

λ = 2/3× 10⁸d, R₀ = 1.33,

p = (cV₀δR₀₎/λ(R0−1)

and β = dδcR₀/λp .

Algorithm
step 1 :
T(0) = T₀, I(0) = I₀, V (0) = V₀ λi(100 ) = 0 (i=1, ..., 3), u₁(0) = 0 =
u₂(0).

step 2 :
for i=1, ..., n-1, do _:
T_i+1=(T_i + hλ)/(1 + h[d + (1 − u₁ⁱ)βV_i]),

I_i+1 =(I_i + h(1 − u₁ⁱ)βV_iT_i+1)/(1 + hδ),

V_i+1 =(V_i + h(1 − u₂ⁱ)pI_i+1)/(1 + hc),

λ_{1ⁿ⁻ⁱ⁻¹} =(λ₁ⁿ⁻ⁱ + h[1 + (1 − u₁ⁱ)βVi+1])/(1 + h[d + (1 − u₁ⁱ)βV_i+1]),

λ₂ⁿ⁻ⁱ⁻¹ =(λ₂ⁿ⁻ⁱ+ hλ₃ⁿ⁻ⁱ (1 − u₂ⁱ)p)/(1 + hδ),

λ₃ⁿ⁻ⁱ⁻¹ =(λ₃ⁿ⁻ⁱ + h(λ₂ⁿ⁻ⁱ⁻¹− λ₁ⁿ⁻ⁱ⁻¹ )(1 − u₁ⁱ)βT_i+1)/(1 + hc),

R1ⁱ⁺¹ =(1/A1)(λ_{1ⁿ⁻ⁱ⁻¹}−λ_{2ⁿ⁻ⁱ⁻¹} )βV_i+1T_i+1,

R2ⁱ⁺¹ =−(1/A2)λ_{3ⁿ⁻ⁱ⁻¹} pI_i+1,

u_1ⁱ⁺¹ = min(1, max(R1ⁱ⁺¹ , 0)),

u_2ⁱ⁺¹ = min(1, max(R2ⁱ⁺¹ , 0)),

end for

step 3 :
for i=1, ..., n-1, write
T^∗(t_i) = T_i, I^∗(t_i) = I_i, V ^∗(t_i) = V_i,

u_1^∗(t_i) = u_1ⁱ, u2^∗(t_i) = u_2ⁱ.

end for

Dear experts;

How can I solve this problem with maple?

restart:

 X[3](0):=6.3096*10^9;
 c:=0.67;
 d:=3.7877*10^(-8);
 delta:=3.259*d;
 lambda:=(2/3)*10^8*d;
 R[0]:=1.33;
 p:=(c*X[3](0)*delta*R[0])/(lambda*(R[0]-1));
beta:=(d*delta*c*R[0])/(lambda*p);

ode:=diff(x[1](t), t)=(lambda-d*x[1](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t)*x[3](t)),
 diff(x[2](t), t) =((1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t)*x[3](t)-delta*x[2](t)),
 diff(x[3](t), t) =((1+psi[3](t)*p*x[2](t)/A[2])*p*x[2](t)-c*x[3](t)),diff(psi[1](t), t) =-1+1/A[1]*beta^2*x[1](t)*(x[3](t))^2*(psi[1](t)-psi[2](t))^2-psi[1](t)*(-d+beta^2*(x[3](t))^2*(psi[1](t)-psi[2](t))/A[1]*x[1](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[3](t))-psi[2](t)*(-beta^2*(x[3](t))^2*(psi[1](t)-psi[2](t))/A[1]*x[1](t)+(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[3](t)),
 diff(psi[2](t), t) =1/A[2]*psi[3](t)^2*p^2*x[2](t)+psi[2](t)*delta-psi[3](t)*(psi[3](t)*p^2/A[2]*x[2](t)+(1+psi[3](t)*p*x[2](t)/A[2])*p),
 diff(psi[3](t), t) = 1/A[1]*beta^2*(x[1](t))^2*x[3](t)*(psi[1](t)-psi[2](t))^2-psi[1](t)*(beta^2*(x[1](t))^2*(psi[1](t)-psi[2](t))/A[1]*x[3](t)-(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t))-psi[2](t)*(-beta^2*(x[1](t))^2*(psi[1](t)-psi[2](t))/A[1]*x[3](t)+(1-beta*x[1](t)*x[3](t)*(psi[1](t)-psi[2](t))/A[1])*beta*x[1](t))+psi[3](t)*c;

ics := x[1](0)=5.5556*10^7, x[2](0)=1.1111*10^7,x[3](0)=6.3096*10^9,psi[1](100)=0,psi[2](100)=0,psi[3](100)=0;

dsolve([ode, ics],numeric);?????????????????????????

Please help me

ode.mws

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