Trouble using ParametricNDSolve in Manipulate

Question

I have troubles to understand how to use Manipulate and ParametricNDSolve to have modulable parameters inside my models. I checked numerous questions on this forum and couldn't find one that satisfies my needs (or, more likely, I didn't understand what to do):

• parametricNDSolve for solving differential equation
• Use ParametricNDSolve with Plotting
• Manipulating a Differential equation

In these examples, the parameters are defined in an equation that isn't a differential one. I don't know if it changes anything in my case but its seems to be at the origin of my problem.

Anyway, here is what I did:

First of all, I've got this model and these constants:

dEc = p1*Ec[t]*(1 - (Ec[t]/Emax)) - d1*Ec[t] - i1*Ic[t]*Ec[t] - r*Vu[t]*Ec[t];
dIc = i1*Ic[t]*Ec[t] + r*Vu[t]*Ec[t] - u1*Ic[t];
dVp = is[t]*b1*u1*Ic[t] - c1*Vp[t];
dUc = p2*Uc[t]*(1 - (Uc[t]/Umax)) - d2*Uc[t] - i2*Yc[t]*Uc[t] - e*Vp[t]*Uc[t];
dYc = i2*Yc[t]*Uc[t] + e*Vp[t]*Uc[t] - u2*Yc[t];
dVu = is[t]*b2*u2*Yc[t] - c2*Vu[t] + s*Vp[t];

parameters = {Emax ->   10000, Umax ->   10000000, p1 ->   0.6, d1 ->   0.003, d2 ->  0.006, u1 ->   0.33, u2 ->   0.33, c1 ->   10, c2 ->   1, b1 ->   6000, b2 ->  6000, i1 ->   0.0000002, i2 ->   0.0000001, e ->   0.000000001, r ->   0.0000001};

Please note that the parameters p2 and sare not defined in the parameters list. It's because that's the ones I want to modify using Manipulate! These parameters are found in equations dUc and dVu

Then, I do a ParametricNDSolve on these equations:

dynamicsmodels =
 ParametricNDSolve[
  Evaluate[{
     Ec'[t] == dEc ,
      Ic'[t] == dIc ,
     Vp'[t] == dVp ,
     Uc'[t] == dUc ,
     Yc'[t] == dYc ,
     Vu'[t] == dVu , 
     Ec[0] == 10000, Ic[0] == 0, Vp[0] == 10, Uc[0] == 10000000, 
     Yc[0] == 0, Vu[0] == 0, is[0] == 0.0005,
      WhenEvent[t == 200, is[t] -> 0.0001]
     } /. parameters],
  {Ec[t], Ic[t], Vp[t], Uc[t], Yc[t], Vu[t]},
  {t, 0, 300},
  {p2, s},
  DiscreteVariables -> {is}[[1]]]

Please note that is[t] is a variable that evolves in the model following time (see my previous question: Having trouble using WhenEvent with NDSolve).

Then, I do a Manipulate:

Manipulate[
 Plot[
  Evaluate[
   {
     Ec[p2, s][t],
     Ic[p2, s][t],
     Vp[p2, s][t],
     Uc[p2, s][t],
     Yc[p2, s][t],
     Vu[p2, s][t]
     } /. dynamicsmodels
   ], {t, 0, 300},
  PlotRange -> {{0, 300}, {0, 10000}},
  PlotStyle -> {Black, Red, Green, Blue, Purple, Orange},
  PlotLegends -> {"Ec", "Ic", "Vp", "Uc", "Yc", "Vu"}], 
 {p2, 1.2, 1.5, Appearance -> "Labeled"},
 {s , 1, 100, Appearance -> "Labeled"} 
 ]

I don't have any error, but no lines either... Am I doing something wrong?

Thanks!

Answer 1

Using ParametricNDSolveValue:

pndsval = ParametricNDSolveValue[
  Evaluate[{Ec'[t] == dEc, Ic'[t] == dIc, Vp'[t] == dVp, 
     Uc'[t] == dUc, Yc'[t] == dYc, Vu'[t] == dVu, Ec[0] == 10000, 
     Ic[0] == 0, Vp[0] == 10, Uc[0] == 10000000, Yc[0] == 0, 
     Vu[0] == 0, is[0] == 0.0005, 
     WhenEvent[t == 200, is[t] -> 0.0001]} /. parameters], {Ec[t], 
   Ic[t], Vp[t], Uc[t], Yc[t], Vu[t]}, {t, 0, 300}, {p2, s}, 
  DiscreteVariables -> {is}[[1]]]; 

 Manipulate[Plot[Evaluate[pndsval[p2, s] /. t -> v], {v, 0, 300}, 
  PlotRange -> {{0, 300}, {0, 10000}}, 
  PlotStyle -> {Black, Red, Green, Blue, Purple, Orange}, 
  PlotLegends -> {"Ec", "Ic", "Vp", "Uc", "Yc", "Vu"}], {p2, 1.2, 1.5,
   Appearance -> "Labeled"}, {s, 1, 100, Appearance -> "Labeled"}]