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Is it possible for NDSolve to solve delay partial differential equations with simple Neumann boundary conditions?

An example I have is as below:

ClearAll["Global`*"]
A1 = 350; A2 = 100;
μ1 = 1/100; α1 = 5/100; β1 = 
 5*10^-6; a2 = 100; β2 = 7*10^-7; μ2 = 
 391*10^-9; α2 = 3/10; γ = 1/100; D1 = 2; D2 = 1;
τ1 = 1/5;
τ2 = 1/6;
omega = ImplicitRegion[0 <= x <= 3, x];
sol = NDSolve[{D[s1[t, x], t] - D1*Laplacian[s1[t, x], x] - 
     A1 - μ1*s1[t, x] - β1*s1[t, x]*I1[t, x] == 
    NeumannValue[0, True],
   D[I1[t, x], t] - 
     D1*Laplacian[I1[t, x], x] - β1*Exp[-μ1*τ1]*
      s1[t - τ1, x]*I1[t - τ1, x] + (μ1 + α1)*
      I1[t, x] == NeumannValue[0, True],
   D[s2[t, x], t] - D2*Laplacian[s2[t, x], x] - 
     A2 - μ2*s2[t, x] - β2*s2[t, x]*I2[t, x] == 
    NeumannValue[0, True],
   D[I2[t, x], t] - 
     D2*Laplacian[I2[t, x], x] - β2*Exp[-μ2*τ2]*
      s2[t - τ2, x]*
      I1[t - τ2, x] + (μ2 + α2 + γ)*I2[t, x] ==
     NeumannValue[0, True],
   D[R2[t, x], t] - 
     D2*Laplacian[I2[t, x], x] - γ*I2[t, x] + μ2*R2[t, x] ==
     NeumannValue[0, True],
   s1[0, x] == 11 + Sin[2 x], 
   I1[t /; t <= 0, x] == 1/10 + 1/100 Sin[2 x], 
   s2[0, x] == 100 + Sin[2 x], I2[t /; t <= 0, x] == 0, R2[0, x] == 0
   }, {s1[t, x], I1[t, x], s2[t, x], I2[t, x], R2[t, x]}, {t, 0, 300},
   Element[x, omega]]

But there is no useful outputs.

From the documents of NDSolve, there are only illustrative examples for delay ordinary differential equations.

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  • $\begingroup$ The numerical solutions to all the dependent variables, s1,s2,I1,I2 and R2, in interpolated function forms as NDSolve usually does, are expected outputs. Since this is a linear system, exact solutions may also be possible. $\endgroup$ – LCFactorization May 6 '17 at 3:26
  • $\begingroup$ Laplacian operator is readily for higher dimensional extensions $\endgroup$ – LCFactorization May 6 '17 at 3:29
  • 2
    $\begingroup$ NDSolve::delpde: Delay partial differential equations are not currently supported by NDSolve. $\endgroup$ – zhk May 6 '17 at 3:31
  • $\begingroup$ thank you. I am not sure whether such feature will be available in the future releases. Delay pdes are still hot topics in recent publications. So it seems in order to use NDSolve to solve the system, one has to do a lot of basic job manually $\endgroup$ – LCFactorization May 6 '17 at 3:36
  • 1
    $\begingroup$ Maybe this is of some kind of help, scicomp.stackexchange.com/questions/23402/… $\endgroup$ – zhk May 6 '17 at 3:44

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