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Clear[Am, As, Aa, \[Alpha], \[Rho], \[Theta]m, \[Theta]s, \
- _; a$ v8 @$ s! T\[CurlyPhi]m, \[CurlyPhi]s, \[Epsilon]]
, l: \- K$ H3 U7 l- H+ f, G\[Gamma]a = 0.1; \[Gamma]m = 0.15; \[Gamma]s =
+ ?2 H4 J5 A9 v* I9 T 1 - \[Gamma]a - \[Gamma]m;
- A& I* `" Y8 n% z\[Epsilon] = 0.04; \[Alpha] = 0.3; \[Rho] = 0.04;
\[Theta]m = 0.75; \[Theta]s = 0.9;
gRate = 0.02;
Am = (gRate + \[Rho])/\[Alpha]; Ba = 4; Bm = 1; Bs = 2.5;
/ ], j& j6 M3 y( h/ s; |ps = Bm/Bs; pa = Bm/Ba;
\[Delta] = 0.03;
B = \!\(TraditionalForm\`\*
. m  I4 S( F2 N+ w* u# P' `FractionBox[
9 j* K2 {. X- p, L3 jRowBox[{
RowBox[{
RowBox[{
% S9 Q4 G0 P5 Z, v. R  o3 Q# @6 qStyleBox["(",
SpanMinSize->1.,
SpanMaxSize->1.],
RowBox[{"1", "\[Minus]", "\[Alpha]"}],
0 }( j5 j" L. ~1 ]- aStyleBox[")",
SpanMinSize->1.,
SpanMaxSize->1.]}], "gRate"}], "+", "\[Rho]"}],
3 ^  D; i- b9 i- A) N- R8 H3 E7 Y      "\[Alpha]"] \[Minus] \[Delta]\);
cap = 10;
csp = (pa*cap)/ps;
D = ((1 \[Minus] \[Alpha])*
( x7 P/ {9 I' ?3 `: K0 q! v' a( y    gRate + \[Rho] - \[Alpha]*\[Delta])/(\[Rho] + gRate);
( _3 \4 r$ u7 l: E! U  [4 Q4 [0 X8 k% t\[CurlyPhi]m = 0.1; \[CurlyPhi]s = 0.1;
Print["*** Initial Values ***"]
E0 = 1.5;
, b" Z1 Y8 f( \; jK0 = E0/B;
hm0 = 0.25; hs0 = 0.25;(* initial values *)
/ D* {( l  U! |0 L2 ]\[Eta]m0 = hm0/K0; \[Eta]s0 = hs0/K0;
5 F/ {# ^! w' Q/ |$ `7 \, N; zxm0 = (B*\[Gamma]m^\[Epsilon]*
' u9 q4 C$ H  a. R5 x0 p   hm0^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(
" k, c# i' v- d% U) B, [& s' w    1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
    hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
      hs0^\[Theta]s)^(1 - \[Epsilon]));
+ V: g" j0 C) Z/ ^xs0 = (B*\[Gamma]s^\[Epsilon]*(ps*
" I7 u2 R' M8 U     hs0^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(
3 S. ~6 A& K7 j0 _    1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
4 b0 W! @, j2 W: `! Z    hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
' i* \) _( s# U+ R5 }& k      hs0^\[Theta]s)^(1 - \[Epsilon]));
1 b+ ], J. k; t/ v# VPrint["\[Eta]_{m,0}=" <> ToString[\[Eta]m0],
* Y# }8 I1 J/ ~ ", \[Eta]_{s,0}=" <> ToString[\[Eta]s0],
", x_{m,0}=" <> ToString[xm0], ", x_{s,0}=" <> ToString[xs0]]
5 j# ]6 t) V  k- DTT = 100;(* end time *)
% e  f& I, G( q- R(* Solve differential equations *)
Sol = NDSolve[{xs'[t] = (1 - \[Epsilon])*
) k* B3 H' u- m1 d     xs[t]*(   (1 - xs[t]/
         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))),
- \3 \& ^) v2 f   xm'[t] == (1 - \[Epsilon])*
. s1 }3 F6 m6 S7 M* o1 V     xm[t]*(   (1 - xm[t]/
( B" C5 j. r. D0 [8 w$ o, @: R          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'[
     t] == \[CurlyPhi]m*
2 @% |4 w+ K8 p& K/ I      xm[t] - (\[CurlyPhi]m + gRate)*\[Eta]m[t], \[Eta]s'[
7 L& N9 f6 j/ F7 J! l+ H4 f" x     t] == \[CurlyPhi]s*xs[t]/ps - (\[CurlyPhi]s + gRate)*\[Eta]s[t],
( |+ W1 o+ Y  j4 _6 A( `/ U   K'[t] == gRate*K[t], hm[t] == \[Eta]m[t]*K[t],
   hs[t] == \[Eta]s[t]*K[t],
$ n& o) {4 p- W/ s7 f   Sa[t] == (\[Gamma]a^\[Epsilon]*(pa)^(1 - \[Epsilon]))/(\[Gamma]a^\
5 ]# c- z# L: [) m6 B\[Epsilon]*pa^(1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
  z9 K- \' ?/ x8 b" v       hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
% a( ~! ?, L! Q8 T! n1 ~, l         hs[t]^\[Theta]s)^(1 - \[Epsilon])) + (\[Gamma]m^\[Epsilon]*
8 O$ r) w3 q5 D: p1 Z      hm[t]^(\[Theta]m*(1 - \[Epsilon]))*pa*
      cap)/((\[Gamma]a^\[Epsilon]*pa^(
         1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
         hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \
* S1 R# O" ^3 h1 N5 v& t$ A\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*
      xm (t)),
$ s/ }) \0 \/ g4 f% i   Sm[t] == (\[Gamma]m^\[Epsilon]*
" S9 G. s6 f9 Z4 Q$ L: O     hm[t]^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(
      1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
      hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
        hs[t]^\[Theta]s)^(1 - \[Epsilon])),
   Ss[t] == (\[Gamma]s^\[Epsilon]*(ps*
2 Z& M& B: X  w1 o% B, K  u- ~        hs[t]^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(
- k- X5 n9 |* w       1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
6 H$ K( f! f' O" d% r- ]- s       hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
         hs[t]^\[Theta]s)^(1 - \[Epsilon])) - (\[Gamma]m^\[Epsilon]*
2 I6 W# |8 C; q# C3 X" m      hm[t]^(\[Theta]m*(1 - \[Epsilon]))*ps*
      csp)/((\[Gamma]a^\[Epsilon]*pa^(
: K+ ?3 W) \" s' k3 g         1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
         hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \
) @% ?2 K2 i# \+ |\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*
: M, [/ H2 ?" t' V% W      xm (t)), xm[0] == xm0,
   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,
7 T6 O4 R. v2 ?1 \2 I7 M    0, TT}]
9 I- P( G4 [. W0 O! `' T4 `Plot[{Evaluate[Sa[t] /. Sol], Evaluate[Sm[t] /. Sol],
3 V! D/ [9 I/ x' F' p" A- n1 Z  Evaluate[Ss[t] /. Sol]}, {t, 0, TT}, AxesOrigin -> {0, 0},
PlotRange -> {0., 0.8}, PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]
Plot[{Evaluate[D*Sa[t] /. Sol],
5 \# [( Q" f+ T- j# n2 w# A6 H- T  Evaluate[(D*Sm[t] + (\[Alpha]*(gRate + \[Delta]))/(\[Rho] +
: F  ?. Z: Z+ w0 C# I; h       gRate)) /. Sol], Evaluate[D*Ss[t] /. Sol]}, {t, 0, TT},
0 `/ [2 M$ C( }/ z; E5 ? AxesOrigin -> {0, 0}, PlotRange -> {0., 0.8},
( a! k2 O! ~# B PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]


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& R! K; E# F9 D; P0 h) n% r
Set::wrsym: Symbol D is Protected.

5 y/ r' W6 J* {8 t% d6 I/ ANDSolve::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.}.
5 A7 @# A' I) O0 G2 c4 x- d
* i. ]3 M- w6 W) u9 @) \7 U

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