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Clear[Am, As, Aa, \[Alpha], \[Rho], \[Theta]m, \[Theta]s, \
) T7 q$ j0 J+ V- f\[CurlyPhi]m, \[CurlyPhi]s, \[Epsilon]]
* B: m% i' R' y4 b4 `+ p\[Gamma]a = 0.1; \[Gamma]m = 0.15; \[Gamma]s =
/ j3 Z$ o% s/ k/ U$ s 1 - \[Gamma]a - \[Gamma]m;
& |' P; ^6 A4 ]; Z5 H3 F\[Epsilon] = 0.04; \[Alpha] = 0.3; \[Rho] = 0.04;
\[Theta]m = 0.75; \[Theta]s = 0.9;
( m! O9 J' ?( |/ _' ?) `gRate = 0.02;
+ [* C% n- q7 X# z, Q$ JAm = (gRate + \[Rho])/\[Alpha]; Ba = 4; Bm = 1; Bs = 2.5;
ps = Bm/Bs; pa = Bm/Ba;
) G* a4 ~- O, h5 x6 {  E. Z\[Delta] = 0.03;
B = \!\(TraditionalForm\`\*
FractionBox[
( g$ F' z6 U! e) wRowBox[{
+ c) b5 p3 Z7 k; R& o' BRowBox[{
% D7 M- F$ ~9 b' Z# ~8 t& h+ pRowBox[{
% @8 d5 Q+ l8 r+ G0 M8 CStyleBox["(",
! Q% ]! H) }' N& _8 [# l& q6 ESpanMinSize->1.,
SpanMaxSize->1.],
RowBox[{"1", "\[Minus]", "\[Alpha]"}],
# u' R- L3 B4 T- V) p6 ^, UStyleBox[")",
SpanMinSize->1.,
SpanMaxSize->1.]}], "gRate"}], "+", "\[Rho]"}],
      "\[Alpha]"] \[Minus] \[Delta]\);
" @: L4 Z, v# Z" U, _1 M( h6 mcap = 10;
csp = (pa*cap)/ps;
* J, U5 b8 Z9 ~6 QD = ((1 \[Minus] \[Alpha])*
( U( e; ?8 ~7 X" U& g8 n! G    gRate + \[Rho] - \[Alpha]*\[Delta])/(\[Rho] + gRate);
8 @3 M; `* i3 \\[CurlyPhi]m = 0.1; \[CurlyPhi]s = 0.1;
; m4 B! M. x) ]7 \Print["*** Initial Values ***"]
( X- r, x( n2 K  \; H  {E0 = 1.5;
K0 = E0/B;
  ^  D7 N, P+ S, p. P  o" ?8 }hm0 = 0.25; hs0 = 0.25;(* initial values *)
\[Eta]m0 = hm0/K0; \[Eta]s0 = hs0/K0;
+ q1 }6 p, s5 mxm0 = (B*\[Gamma]m^\[Epsilon]*
) H" p# Z8 S8 ~   hm0^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(
    1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
0 A+ ]8 N: y! g' L2 F    hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
' J7 j, C% C3 C9 u% X1 _      hs0^\[Theta]s)^(1 - \[Epsilon]));
# A* c) X  t9 i2 L: o; vxs0 = (B*\[Gamma]s^\[Epsilon]*(ps*
; a  y4 k# R  ^& E! x/ F  B, F* ?; x     hs0^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(
    1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
6 i4 _; A" z! Y8 `6 k3 R: Y    hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
& k0 `  o) K) _% g0 \8 N# a8 L      hs0^\[Theta]s)^(1 - \[Epsilon]));
0 z( u% i( Q8 C5 k  r) u& S+ NPrint["\[Eta]_{m,0}=" <> ToString[\[Eta]m0],
", \[Eta]_{s,0}=" <> ToString[\[Eta]s0],
", x_{m,0}=" <> ToString[xm0], ", x_{s,0}=" <> ToString[xs0]]
5 b8 J0 x5 p4 i; A# {, HTT = 100;(* end time *)
8 F! y" K# `# q( i$ y(* Solve differential equations *)
Sol = NDSolve[{xs'[t] = (1 - \[Epsilon])*
     xs[t]*(   (1 - xs[t]/
         B)*(\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 1) -
4 o4 Z* `/ t+ k- V. g( m% U         xm[t]/B \[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1))),
   xm'[t] == (1 - \[Epsilon])*
* L+ W* J( ?* k$ R     xm[t]*(   (1 - xm[t]/
          B)*\[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1) -
9 @+ S* c  n; V) V) }  B0 e1 w       xs[t]/B*\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) -
          1) ), \[Eta]m'[
     t] == \[CurlyPhi]m*
      xm[t] - (\[CurlyPhi]m + gRate)*\[Eta]m[t], \[Eta]s'[
7 i% R) ~- K4 s8 N% M" u     t] == \[CurlyPhi]s*xs[t]/ps - (\[CurlyPhi]s + gRate)*\[Eta]s[t],
   K'[t] == gRate*K[t], hm[t] == \[Eta]m[t]*K[t],
   hs[t] == \[Eta]s[t]*K[t],
   Sa[t] == (\[Gamma]a^\[Epsilon]*(pa)^(1 - \[Epsilon]))/(\[Gamma]a^\
% `- c3 q2 p/ y/ u9 {7 s6 b8 E; a\[Epsilon]*pa^(1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
& \- C4 _2 f1 E) A5 L6 A8 B0 B       hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
9 D  E0 P5 f& \+ S" i% G& k         hs[t]^\[Theta]s)^(1 - \[Epsilon])) + (\[Gamma]m^\[Epsilon]*
      hm[t]^(\[Theta]m*(1 - \[Epsilon]))*pa*
- V% M. N# h+ x# p9 x6 ~) ~3 m2 `      cap)/((\[Gamma]a^\[Epsilon]*pa^(
8 }/ y2 o$ k8 n* F3 u         1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
         hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \
\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*
      xm (t)),
# g( B5 z" W3 ^9 J7 f- ~2 i; A   Sm[t] == (\[Gamma]m^\[Epsilon]*
% P) K! U5 m% D3 ]/ v, H, m$ \     hm[t]^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(
      1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
" l# _: S8 e  h) C" G      hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
        hs[t]^\[Theta]s)^(1 - \[Epsilon])),
   Ss[t] == (\[Gamma]s^\[Epsilon]*(ps*
        hs[t]^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(
+ K) u5 [( J+ {' W0 W1 z       1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
       hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
         hs[t]^\[Theta]s)^(1 - \[Epsilon])) - (\[Gamma]m^\[Epsilon]*
      hm[t]^(\[Theta]m*(1 - \[Epsilon]))*ps*
% D5 n1 ~5 T4 p" _) h      csp)/((\[Gamma]a^\[Epsilon]*pa^(
- y4 K( U8 L# j* w3 O& D  z         1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
3 m0 ^! F! ]$ i7 \& e# m         hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \
\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*
3 k2 k1 v$ J: ?* }- U      xm (t)), xm[0] == xm0,
7 x; V1 F# \8 o" |6 ~   xs[0] == xs0, \[Eta]m[0] == \[Eta]m0, \[Eta]s[0] == \[Eta]s0,
) s# E6 L  e% ?* E$ x2 m   K[0] == K0}, {xm, xs, \[Eta]m, \[Eta]s, K, hm, hs, Sa, Sm, Ss}, {t,
    0, TT}]
Plot[{Evaluate[Sa[t] /. Sol], Evaluate[Sm[t] /. Sol],
  Evaluate[Ss[t] /. Sol]}, {t, 0, TT}, AxesOrigin -> {0, 0},
PlotRange -> {0., 0.8}, PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]
; \+ }# K# n/ LPlot[{Evaluate[D*Sa[t] /. Sol],
- r2 z$ z& j' L5 m. P2 ]  Evaluate[(D*Sm[t] + (\[Alpha]*(gRate + \[Delta]))/(\[Rho] +
       gRate)) /. Sol], Evaluate[D*Ss[t] /. Sol]}, {t, 0, TT},
AxesOrigin -> {0, 0}, PlotRange -> {0., 0.8},
( l6 N" S0 v9 O! ]; y PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]
4 [: m, c6 l0 d  p$ w( T' D

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Set::wrsym: Symbol D is Protected.

NDSolve::deqn: Equation or list of equations expected instead of 0.96 (1-6.66667 xs[t]) xs[t] (-0.5 xm[t] (-1+xm[t]/\[Eta]m[t])+0.09 (-1+(2.5 xs[t])/\[Eta]s[t])) in the first argument {0.96 (1-6.66667 xs[t]) xs[t] (-0.5 xm[t] (-1+xm[t]/\[Eta]m[<<1>>])+0.09 (-1+(2.5 xs[t])/\[Eta]s[<<1>>])),<<13>>,K[0]==10.}.


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