Nonlinear ODE minimization - boundary value problem
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Hello, I'm trying to implement the system used in chemotherapy drug administration, suggested in the paper (see attachment) by L.G.dePillis & A.Radunskaya.
The equaitons are :
N_dot = r2*N*(1 -b2*N) -c4*T*N -a3*(1-exp(-u))*N;
T_dot = r1*T*(1 -b1*T) -c2*I*T -c3*T*N -a2*(1-exp(-u))*T;
I_dot = s +ro*I*T/(alpha +T) -c1*I*T -d1*I -a1*(1-exp(-u))*I;
u_dot = v - d2*u;
The objective function to be minimized at the final time (tf) is :
J(tf) = T(tf)
under the constraint :
N >= 0.75; % for every t
Also in p.13, there is an analysis of the Hamiltonian and the co-state variables p1,p2,p3,p4.
Their boundary values for tf are :
p1(tf) = 0;
p2(tf) = 1;
p3(tf) = 0;
p4(tf) = 0;
Then the control equation is p4 and the drug (v) is administered as follows :
if p4>0
v = 0;
elseif p4<0
v = 1; % maximum dosage
end
The paper says this is a two point boundary value problem.
How can I implement it in Matlab (or Simulink)? I think some information is missing to use bvp4c.
Thank you.
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2020-1-5
2020-1-5
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