Solving a non-linear ODE with a non-trivial coupling between the state variables

Question

I'm trying to solve an ODE where I need to integrate over the entire solution (up to the calculated time step) of one of the state variables.

The equations look as follows

I outline below two pieces of code.

The first code below is without the complexity I'm referring to (bolded in the equation description above), and it runs well.

\[Delta][t_] := 1 - 1/4 (1 - Exp[-(t/10)]);
d\[Delta][t_] := -(1/40) Exp[-(t/10)];
V[t_] := 0.1 + 5/(1 - Exp[-\[Delta][t]]); 

c[\[Phi]_, A_?NumericQ, u_?NumericQ] := 
  Module[{}, 
   N@If[u == 0, 1/A, 
     u/Sqrt[4 A] (Exp[-Sqrt[A] u Cos[\[Phi]]]/
       BesselI[1, u Sqrt[A]]) ]] ; 
uSS[A_?NumericQ, u_?NumericQ] := 
  2 NIntegrate[
    Cos[\[Phi]]/(1 + c[\[Phi], A, u]), {\[Phi], -\[Pi] + 
      10^-7, \[Pi] - 10^-7}, Method -> "LocalAdaptive"];

(*Define the differential equations*)
dAdt[A_?NumericQ, V_, u_?NumericQ, 
   t_] := (2 A)/3 (1 - 1/(4 V)) d\[Delta][t] - 
   A^2/(18 \[Pi]) (A^3/
       V^2 (2 - 
         1/\[Pi] NIntegrate[
           1/(1 + c[\[Phi], A, u]), {\[Phi], -\[Pi] + 10^-7, \[Pi] - 
             10^-7}, Method -> "LocalAdaptive"]) - 8 \[Pi]);

dUdt[A_?NumericQ, u_?NumericQ] := -10 (u - uSS[A, u]); 
{Asol, Usol} = 
  NDSolveValue[{A'[t] == dAdt[A[t], V[t], u[t], t], 
    u'[t] == dUdt[A[t], u[t]], A[0] == 5, u[0] == N@10^-4}, {A, 
    u}, {t, 0, 50}, 
   Method -> {"EquationSimplification" -> "Residual"}];
Plot[{Asol[t], V[t], Usol[t]}, {t, 0, 50}, PlotRange -> All, 
 PlotLegends -> "Expressions"]

The second piece of code below is my attempt to include the non-trivial non-linear addition of the dependence in the state variable A in the equation. This code is not working.

Int[t_, A_] := 
  NIntegrate[A'[s] Exp[-((t - s))], {s, 0, t}, 
   Method -> "LocalAdaptive"];
\[Delta][t_, A_] := 
  1 + 1/40 ((A - 1) + Int[t, A]) - 1/4 (1 - Exp[-(t/10)]);
d\[Delta][t_, A_] := 1/40 (A'[t] - Int[t, A] - Exp[-(t/10)]);
V[t_, A_] := 0.1 + 5/(1 - Exp[-\[Delta][t, A]]); 

c[\[Phi]_, A_?NumericQ, u_?NumericQ] := 
  Module[{}, 
   N@If[u == 0, 1/A, 
     u/Sqrt[4 A] (Exp[-Sqrt[A] u Cos[\[Phi]]]/
       BesselI[1, u Sqrt[A]]) ]] ; 
uSS[A_?NumericQ, u_?NumericQ] := 
  2 NIntegrate[
    Cos[\[Phi]]/(1 + c[\[Phi], A, u]), {\[Phi], -\[Pi] + 
      10^-7, \[Pi] - 10^-7}, Method -> "LocalAdaptive"];

(*Define the differential equations*)
dAdt[A_?NumericQ, V_, u_?NumericQ, 
   t_] := (2 A)/3 (1 - 1/(4 V)) d\[Delta][t, A] - 
   A^2/(18 \[Pi]) (A^3/
       V^2 (2 - 
         1/\[Pi] NIntegrate[
           1/(1 + c[\[Phi], A, u]), {\[Phi], -\[Pi] + 10^-7, \[Pi] - 
             10^-7}, Method -> "LocalAdaptive"]) - 8 \[Pi]);

dUdt[A_?NumericQ, u_?NumericQ] := -10 (u - uSS[A, u]); 
{Asol, Usol} = 
  NDSolveValue[{A'[t] == dAdt[A[t], V[t, A[t]], u[t], t], 
    u'[t] == dUdt[A[t], u[t]], A[0] == 5, u[0] == N@10^-4}, {A, 
    u}, {t, 0, 50}, 
   Method -> {"EquationSimplification" -> "Residual"}];
Plot[{Asol[t], V[t, Asol[t]], Usol[t]}, {t, 0, 50}, PlotRange -> All, 
 PlotLegends -> "Expressions"]

I wish to find a way to integrate in the equation this new dependece in A, and have an explanation of why and how to do this in mathematica.