Solve differential equation system for HIV treatment model?

Questions
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1

Dear All,

I was working on a project about optimal strategies for HIV treatment, models used from [Butler, Kirschner, and Lenhart] 1997. This model explains the spread of HIV viruses in the human body, where there is one control function u(t).

model.png
model.png887Ă—404 38.2 KB

My work is following pontryagin maximum principle. But i have a problem solving the differential equation system, where there are 6 differential equations with 6 initial conditions. Here i use software Mathematica 11 when I execute the code there is no error that appears and he just returning DSolve code that i write.

DSolve[{eq1, eq2, eq3, eq4, eq5, eq6, T[0] == 800, Ti[0] == 0.04, 
  V[0] == 1.5, l1[20] == 0, l2[20] == 0, l3[20] == 0}, {l1[t], l2[t], 
  l3[t], T[t], Ti[t], V[t]}, t]

I cannot guarantee that the analytical solution exists, but is there something wrong with code I wrote? Or is there an alternative solution to complete the differential equation system?

I hope you are pleased to check the file that I attached.

Many thanks .

Control Optimal for HIV Treatment.nb (25.6 KB)

ga ada error.png
ga ada error.png1289Ă—517 15.4 KB

2

A few issues:

  1. I doubt DSolve will be able to solve this system of equations. You should try NDSolve, as well as set an initial and final time: e.g. {t, 0, 1}

  2. Inside of your notebook, u[t]= should probably be u[t_] :=

  3. From a scientific viewpoint: do you have “Terminal Conditions” to make a BVP rather than an IVP? These are often found in Pontryagin-type problems, often solved with the Shooting Method of NDSolve.