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Clear[Am, As, Aa, \[Alpha], \[Rho], \[Theta]m, \[Theta]s, \
2 v1 F# ?; z3 k9 b/ C\[CurlyPhi]m, \[CurlyPhi]s, \[Epsilon]]
* @' ?0 A6 c) K; d\[Gamma]a = 0.1; \[Gamma]m = 0.15; \[Gamma]s =
9 c8 D5 E& _$ Z$ r  N+ j  K7 U 1 - \[Gamma]a - \[Gamma]m;
\[Epsilon] = 0.04; \[Alpha] = 0.3; \[Rho] = 0.04;
9 s4 f: S6 k7 ~; z' T- z9 \\[Theta]m = 0.75; \[Theta]s = 0.9;
gRate = 0.02;
Am = (gRate + \[Rho])/\[Alpha]; Ba = 4; Bm = 1; Bs = 2.5;
9 v2 m+ E4 D3 {2 [ps = Bm/Bs; pa = Bm/Ba;
# c  U/ W8 o% R" Q\[Delta] = 0.03;
) V5 o$ P' T* IB = \!\(TraditionalForm\`\*
" p/ G3 J) u+ ^5 WFractionBox[
$ I& o, I6 c) o* q2 Q8 sRowBox[{
RowBox[{
RowBox[{
& K5 |- R& A. K! `% RStyleBox["(",
SpanMinSize->1.,
SpanMaxSize->1.],
RowBox[{"1", "\[Minus]", "\[Alpha]"}],
8 z3 L8 a/ ]* ?6 \. b, o: x/ rStyleBox[")",
* f' d- |6 b9 K7 uSpanMinSize->1.,
' l' Y0 m6 t) Z- VSpanMaxSize->1.]}], "gRate"}], "+", "\[Rho]"}],
      "\[Alpha]"] \[Minus] \[Delta]\);
cap = 10;
: A. b+ V. k( s+ q; Wcsp = (pa*cap)/ps;
D = ((1 \[Minus] \[Alpha])*
% B# l: x( P& f6 ]  V    gRate + \[Rho] - \[Alpha]*\[Delta])/(\[Rho] + gRate);
( N3 Y6 u0 T+ M& d% D% ^\[CurlyPhi]m = 0.1; \[CurlyPhi]s = 0.1;
Print["*** Initial Values ***"]
6 H2 |# [6 f; ~( V7 RE0 = 1.5;
K0 = E0/B;
) y- C  t% M; `  V4 X1 l# q/ Z, |hm0 = 0.25; hs0 = 0.25;(* initial values *)
\[Eta]m0 = hm0/K0; \[Eta]s0 = hs0/K0;
& Q4 k* o8 w, Lxm0 = (B*\[Gamma]m^\[Epsilon]*
3 j5 \' W6 @' Z, p9 m' v/ V! `   hm0^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(
' I1 E5 Z. |7 [2 l    1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
    hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
      hs0^\[Theta]s)^(1 - \[Epsilon]));
3 G# n% d# A4 d6 j, }5 bxs0 = (B*\[Gamma]s^\[Epsilon]*(ps*
) b4 E7 N$ x8 Y9 ^/ [     hs0^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(
    1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
# r9 ]# F4 K# @  P; ]- R% H/ R5 J    hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
      hs0^\[Theta]s)^(1 - \[Epsilon]));
$ C8 S# h: y" i$ v# _; yPrint["\[Eta]_{m,0}=" <> ToString[\[Eta]m0],
8 y: j- D- r5 ]7 |! | ", \[Eta]_{s,0}=" <> ToString[\[Eta]s0],
", x_{m,0}=" <> ToString[xm0], ", x_{s,0}=" <> ToString[xs0]]
TT = 100;(* end time *)
(* Solve differential equations *)
* f# M8 t( Y* P5 R+ a$ h; rSol = NDSolve[{xs'[t] = (1 - \[Epsilon])*
4 A% b9 [- k; [- O     xs[t]*(   (1 - xs[t]/
$ s7 Z0 Z. q. i9 {) A3 ~4 U         B)*(\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) - 1) -
         xm[t]/B \[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1))),
   xm'[t] == (1 - \[Epsilon])*
/ |1 d9 d( O* [, G1 Y' B9 s" W, q0 J     xm[t]*(   (1 - xm[t]/
          B)*\[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1) -
       xs[t]/B*\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) -
          1) ), \[Eta]m'[
9 ^% i9 s; w. z( v8 G  N" V6 w     t] == \[CurlyPhi]m*
      xm[t] - (\[CurlyPhi]m + gRate)*\[Eta]m[t], \[Eta]s'[
     t] == \[CurlyPhi]s*xs[t]/ps - (\[CurlyPhi]s + gRate)*\[Eta]s[t],
6 Q( [8 e# h4 p* l, G! n, O9 U3 e   K'[t] == gRate*K[t], hm[t] == \[Eta]m[t]*K[t],
   hs[t] == \[Eta]s[t]*K[t],
& s8 a4 _1 D3 }   Sa[t] == (\[Gamma]a^\[Epsilon]*(pa)^(1 - \[Epsilon]))/(\[Gamma]a^\
\[Epsilon]*pa^(1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
       hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
9 e! H$ U1 V* l$ l% ~& k         hs[t]^\[Theta]s)^(1 - \[Epsilon])) + (\[Gamma]m^\[Epsilon]*
: k* p! ~4 K1 s+ \+ c) i      hm[t]^(\[Theta]m*(1 - \[Epsilon]))*pa*
- g  z+ R6 C0 A" V; X; L6 c# t      cap)/((\[Gamma]a^\[Epsilon]*pa^(
         1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
         hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \
$ D+ c( o4 }1 Y# s" K\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*
      xm (t)),
   Sm[t] == (\[Gamma]m^\[Epsilon]*
( _  f6 `3 B5 W- T, B' g( m     hm[t]^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(
* j+ p& K/ E6 ^3 O, W) T      1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
! A" X3 E+ Z* o1 h; J: ^  X; R+ g      hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
- O. Y; O( \6 {        hs[t]^\[Theta]s)^(1 - \[Epsilon])),
   Ss[t] == (\[Gamma]s^\[Epsilon]*(ps*
        hs[t]^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(
       1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
. E/ a; I& ^; O, g       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*
4 U% a/ ]' C) q% u, x1 e. V) {      csp)/((\[Gamma]a^\[Epsilon]*pa^(
. c: ^$ G: C/ k5 i         1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
         hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \
\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*
  I2 l' c+ M0 F  P# R  y' Z      xm (t)), xm[0] == xm0,
" L7 y( u+ m7 w- \: \   xs[0] == xs0, \[Eta]m[0] == \[Eta]m0, \[Eta]s[0] == \[Eta]s0,
   K[0] == K0}, {xm, xs, \[Eta]m, \[Eta]s, K, hm, hs, Sa, Sm, Ss}, {t,
    0, TT}]
; q+ s& p) M$ w* V' N# v  l1 B: m5 E7 h% S1 JPlot[{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}]}]
. u$ `, X. F- N/ M, m4 y  BPlot[{Evaluate[D*Sa[t] /. Sol],
  {* ^0 B" j" j* Y  Evaluate[(D*Sm[t] + (\[Alpha]*(gRate + \[Delta]))/(\[Rho] +
8 K  N. B# n7 Z. {" y       gRate)) /. Sol], Evaluate[D*Ss[t] /. Sol]}, {t, 0, TT},
AxesOrigin -> {0, 0}, PlotRange -> {0., 0.8},
0 \- b! G9 J( K; `* h8 h4 Y PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]
" }6 l' _0 ^# M' X  B: X2 q


6 r% j7 k7 p* ^* I* X( P, h7 _& a
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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