I an unable to prot the optimal  control function and the controls individualy for the diterministic mathematical model with an two or more optimal control. May  any one can give me a sample program on it. Such us the following figure

You may give me direction even.

Dear Brothers and Sisters,

I faced warnning while simulating the code below was running

restart;
with(plots);
beta := 0.143e-1; delta := 0.7e-1; PI := 2.5; mu := 0.16e-1; tau := .7; rho := 0.4e-3; epsilon := .15; sigma[2] := 0.2e-1; sigma[1] := 0.1e-3; eta := 0.1e-1;
a[1] := 2; a[2] := 5; w[1] := 10; w[2] := 50; w[3] := 20; T := 4;

u[1] := min(max(0, z), 1); z := beta*(1-u[3])*s(t)*(sigma[2]*e(t)+sigma[1]*i[t])*(lambda[2](t)-lambda[1](t))/w[1]; u[2] := min(max(0, c), 1); c := (lambda[2](t)*e(t)+beta*i(t)+lambda[4](t)*((1-tau)*delta*e(t)+epsilon*i(t))+lambda[3](t)*(delta*tau*e(t)+epsilon*i(t)))/w[2]+lambda[2](t)*e(t)/w[2]; u[3] := min(max(0, e), 1); e := (beta*(1-u[1])*s(t)*sigma[2]*e(t)+sigma[1]*i[t])/w[3];
Error, recursive assignment

sys := diff(s(t), t) = PI+eta*r(t)-((1-u[1])*(1-u[1]))*beta*(sigma[1]*i(t)+sigma[2]*e(t))*s(t)-mu*s(t), diff(e(t), t) = (((1-u[1])*(1-u[1]))*beta*beta)*(sigma[1]*i(t)+sigma[2]*e(t))*s(t)-(u[2]+u[3]+delta+mu)*e(t), diff(i(t), t) = (1-u[2])*tau*delta*e(t)-(u[2]+u[3]+epsilon+rho+mu)*i(t), diff(r(t), t) = (1-u[2])*(1-tau)*delta*e(t)+(1-u[2])*epsilon*i(t)-(mu+eta)*r(t), diff(lambda[1](t), t) = lambda[1]*((1-u[3])*(1-u[1])*beta*(e*sigma[2]+i*sigma[1])-mu)-lambda[2]*(1-u[3])*(1-u[1])*beta*(e*sigma[2]+i*sigma[1]), diff(lambda[2](t), t) = -a[1]+lambda[1]*((1-u[3])*(1-u[1])*beta*sigma[2]*s-lambda[2]*(1-u[3])*(1-u[1])*beta*sigma[2]*s-u[2]-u[3]-delta-mu)-lambda[3]*(1-u[2])*tau*delta-lambda[4]*(1-u[2])*(1-tau)*delta, diff(lambda[3](t), t) = -a[2]+lambda[1]*(1-u[3])*(1-u[1])*beta*sigma[1]*s-lambda[2]*(1-u[3])*(1-u[1])*beta*sigma[1]*s+lambda[3]*(u[2]+u[3]+epsilon+rho+mu)-lambda[4]*(1-u[2])*epsilon, diff(lambda[4](t), t) = -lambda[1]*eta+lambda[4]*(mu+eta), s(0) = 1000000, e(0) = 1000, i(0) = 89, r(0) = 16, lambda[1](T) = 0, lambda[2](T) = 0, lambda[3](T) = 0, lambda[4](T) = 0;
p1 := dsolve({sys}, type = numeric, method = bvp[midrich], abserr = .1);
Error, (in dsolve/numeric/bvp/convertsys) e(t) and e cannot both appear in the given ODE
p2o := odeplot(p1, [t, i(t)], 0 .. 2, numpoints = 100, labels = ["Time (months)", "i"], labeldirections = [horizontal, vertical], style = line, color = red, axes = boxed);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
plots[display](p2o);

May I get your help please? Thank you in advance. Lokking forward...

     Dear Sir/Madam,

I have faced a problem while using Maple 18. The  warning is the following

Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters)

This is the code

restart;
with(plots);
beta := 0.2e-1; delta := .5; PI := 10000; mu := 0.16e-1; tau := 0.3e-1; rho := 0.4e-1; epsilon := 0.4e-1; sigma[1] := 0.1e-2; sigma[2] := 0.2e-2; eta := 0.6e-1;
sys := {diff(e(t), t) = beta*(sigma[1]*i(t)+sigma[2]*e(t))*s(t)-(delta+mu)*e(t), diff(i(t), t) = tau*delta*e(t)-(epsilon+rho+mu)*i*t, diff(r(t), t) = (1-tau)*delta*e(t)+epsilon*i(t)-(mu+eta)*r(t), diff(s(t), t) = PI+eta*r(t)-beta*(sigma[1]*i(t)+sigma[2]*e(t))*s(t)-mu*s(t), e(0) = 148, i(0) = 74, r(0) = 14, s(0) = 4110};
p1 := dsolve(sys, numeric, method = rkf45, output = procedurelist);
Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters)
Error, (in dsolve/numeric) i(t) and i cannot both appear in the given ODE
p2o := odeplot(p1, [t, s(t)], 0 .. 4, numpoints = 100, labels = ["Time (months)", " Infected  "], labeldirections = [horizontal, vertical], style = line, color = red, axes = boxed);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

plots[display](p2o);

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/nnn.mw .

Download nnn.mw

Hello Dear Brothers and Sistors,

Can you help me giving a maple program to plot cost function  of a an optimal control modeling ?

Looking forward.

Regards,

Hello,

I'm trying to solve a system of ODE in a model of infectious disease. But, unfortunately, when I try to plot the curves, I get the following error message: Error, (in fproc) unable to store '-1.*HFloat(0.0)[1]' when datatype=float[8]. The code is here

restart;
with(plots);
Q := 1000; a := .9; b := 0.8e-3; mu := 0.247e-2; k := .2; y := 0.2e-1; e := .5; g := .5; T := 8; n := 100;
sigma[1] := 0.5e-1; sigma[2] := 0.9e-1; alpha[1] := 0.52e-2; alpha[2] := 0.52e-2; delta[1] := .8; delta[2] := .904; delta[3] := .8; c[1] := 50; c[2] := 250; c[3] := 50; w[1] := 140; w[2] := 130; w[3] := 150; w[4] := 160;
u[1] := min(max(0, z), 1); z := (a*i[p](t)*(i[p](t)+i[pm](t))*(lambda[4](t)-lambda[3](t))+a*s(t)*(i[p](t)+i[pm](t))*(lambda[1](t)-lambda[2](t)))/(n.w[1]); u[2] := min(max(0, c), 1); c := (b*(i[m](t)+i[pm](t))*s(t)*(lambda[3](t)-lambda[1](t))+b*(i[m](t)+i[pm](t))*i[p](t)*(lambda[4](t)-lambda[2](t)))/(n.w[2]); u[3] := min(max(0, j), 1); j := (i[p](t)*lambda[2](t)+i[pm](t)*(lambda[4](t)-lambda[7](t))-(i[p](t)+i[pm](t))*lambda[5](t))/w[3]; u[4] := min(max(0, o), 1); o := (i[m](t)*lambda[3](t)-i[pm](t)*(lambda[4](t)-lambda[7](t))-(i[m](t)+i[pm](t))*lambda[6](t))/w[4]; u[2] := 0; u[3] := 0;
;
sys := diff(s(t), t) = Q+delta[1]*r[p](t)+delta[2]*r[m](t)+delta[3]*r[pm](t)-(a*(1-u[1])*(i[p](t)+i[pm](t))/n+b*(1-u[2])*(i[m](t)+i[pm](t))/n+mu)*s(t), diff(i[p](t), t) = (1-u[1])*a*(i[p](t)+i[pm](t))*s(t)/n-(1-u[2])*b*(i[m](t)+i[pm](t))*i[p](t)/n-(sigma[1]+u[3])*i[p](t)-(alpha[1]+mu)*i[p](t), diff(i[m](t), t) = (1-u[2])*b*(i[m](t)+i[pm](t))*s(t)/n-(1-u[1])*a*(i[p](t)+i[pm](t))*i[m](t)/n-(sigma[2]+u[4])*i[m](t)-(alpha[2]+mu)*i[m](t), diff(i[pm](t), t) = (1-u[2])*b*(i[m](t)+i[pm](t))*i[p](t)/n+(1-u[1])*a*(i[p](t)+i[pm](t))*i[m](t)/n-(y+u[3]+u[4])*i[pm](t)-(alpha[1]+alpha[2]+mu)*i[pm](t), diff(r[p](t), t) = (sigma[1]+u[3])*i[p](t)+(e*y+u[3])*i[pm](t)-(delta[1]+mu)*r[p](t), diff(r[m](t), t) = (sigma[2]+u[4])*i[m](t)+(y*g*(1-e)+u[4])*i[pm](t)-(delta[2]+mu)*r[m](t), diff(r[pm](t), t) = (y*(1-g)*(1-e)+u[3]+u[4])*i[pm](t)-(delta[3]+mu)*r[pm](t), diff(lambda[1](t), t) = lambda[1](t)*(a*(1-u[1])*(i[p](t)+i[pm](t))/n+b*(1-u[2])*(i[m](t)+i[pm](t))/n+mu)-lambda[2](t)*(1-u[1])*a*(i[p](t)+i[pm](t))/n-lambda[3](t)*(1-u[2])*b*(i[m](t)+i[pm](t))/n, diff(lambda[2](t), t) = -c[1]+lambda[1](t)*(1-u[1])*a*s(t)/n-lambda[2](t)*((1-u[1])*a*s(t)/n+b*(1-u[2])*(i[m](t)+i[pm](t))/n+sigma[1]+u[3]+alpha[1]+mu)-lambda[4](t)*(b*(1-u[2])*(i[m](t)+i[pm](t))/n+(1-u[1])*a*i[m](t)/n)-lambda[5](t)*(sigma[1]+u[3]), diff(lambda[3](t), t) = -c[2]+lambda[1](t)*(1-u[2])*b*s(t)/n+lambda[2](t)*(1-u[2])*b*i[p](t)/n-lambda[3](t)*(u[4]+alpha[2]+sigma[2]+a*(1-u[1])*(i[p](t)+i[pm](t))/n-(1-u[2])*b*s(t)/n)-lambda[4](t)*((1-u[2])*b*i[p](t)/n+a*(1-u[1])*(i[p](t)+i[pm](t))/n)-lambda[6](t)*(sigma[2]+u[4]), diff(lambda[4](t), t) = -c[3]+lambda[1](t)*((1-u[1])*a*s(t)/n+(1-u[2])*b*s(t)/n)-lambda[2](t)*((1-u[2])*b*i[p](t)/n+(1-u[1])*a*s(t)/n)-lambda[2](t)*((1-u[2])*a*i[m](t)/n+b*(1-u[1])*s(t)/n)-lambda[4](t)*(y+u[3]+u[4]+alpha[1]+alpha[2]+mu-(1-u[2])*b*i[p](t)/n-b*(1-u[1])*i[m](t)/n)-lambda[5](t)*(e*y+u[3])-lambda[6](t)*(y*g*(1-e)+u[4])-lambda[7](t)*(y*(1-g)*(1-e)+u[3]+u[4]), diff(lambda[5](t), t) = -lambda[1](t)*delta[1]+lambda[5](t)*(delta[1]+mu), diff(lambda[6](t), t) = -lambda[1](t)*delta[2]+lambda[6](t)*(delta[2]+mu), diff(lambda[7](t), t) = -lambda[1](t)*delta[3]+lambda[7](t)*(delta[3]+mu), i[p](0) = 300, i[m](0) = 200, i[pm](0) = 150, r[p](0) = 200, r[m](0) = 150, r[pm](0) = 150, s(0) = 1000, lambda[1](T) = 0, lambda[2](T) = 0, lambda[3](T) = 0, lambda[4](T) = 0, lambda[5](T) = 0, lambda[6](T) = 0, lambda[7](T) = 0;
p1 := dsolve({sys}, type = numeric, method = bvp[midrich], abserr = 0.1e-5, maxmesh = 2400);
Error, (in fproc) unable to store '-1.*HFloat(0.0)[1]' when datatype=float[8]
p2o := odeplot(p1, [t, i[p](t)], 0 .. 3, numpoints = 100, labels = ["Time (Months)", " Population"], labeldirections = [horizontal, vertical], style = line, color = green, axes = boxed);
 

Can anyone help me please? I read some related problems here, but couldnt find a solution yet.

Thanks for your time

Best regards