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Clear[Am, As, Aa, \[Alpha], \[Rho], \[Theta]m, \[Theta]s, \
7 U6 w; l' \, r% i; o\[CurlyPhi]m, \[CurlyPhi]s, \[Epsilon]]
- |8 U) Q" r) T( g\[Gamma]a = 0.1; \[Gamma]m = 0.15; \[Gamma]s =
1 - \[Gamma]a - \[Gamma]m;
\[Epsilon] = 0.04; \[Alpha] = 0.3; \[Rho] = 0.04;
\[Theta]m = 0.75; \[Theta]s = 0.9;
gRate = 0.02;
- z5 u7 t) d+ t( q- uAm = (gRate + \[Rho])/\[Alpha]; Ba = 4; Bm = 1; Bs = 2.5;
ps = Bm/Bs; pa = Bm/Ba;
& ~, K" q: j( c* Z, z\[Delta] = 0.03;
B = \!\(TraditionalForm\`\*
+ P4 w: v3 l+ U  nFractionBox[
RowBox[{
, C, _( ?/ w$ sRowBox[{
7 [; B: K; c: S4 X4 E) z1 nRowBox[{
StyleBox["(",
SpanMinSize->1.,
SpanMaxSize->1.],
5 \: z& Q8 ~5 K; IRowBox[{"1", "\[Minus]", "\[Alpha]"}],
StyleBox[")",
SpanMinSize->1.,
SpanMaxSize->1.]}], "gRate"}], "+", "\[Rho]"}],
. e' G2 W$ Q+ E  f$ d+ T      "\[Alpha]"] \[Minus] \[Delta]\);
cap = 10;
2 D, x' W+ y8 y) v. Ncsp = (pa*cap)/ps;
7 \& x: r$ W3 g$ J4 @, E' n) f3 V; xD = ((1 \[Minus] \[Alpha])*
8 ^5 }3 h) Z" C. _  z$ f    gRate + \[Rho] - \[Alpha]*\[Delta])/(\[Rho] + gRate);
+ R! q+ H: r8 j5 Z! D1 v\[CurlyPhi]m = 0.1; \[CurlyPhi]s = 0.1;
6 S# ^+ V- r* ]! e& A+ APrint["*** Initial Values ***"]
4 M1 o% ^. J! s& aE0 = 1.5;
% b" m! m+ U' {) [# T& kK0 = E0/B;
; S8 ~7 h3 s( `' @* G3 e: ?0 khm0 = 0.25; hs0 = 0.25;(* initial values *)
\[Eta]m0 = hm0/K0; \[Eta]s0 = hs0/K0;
/ m2 S; Z( G3 o8 r+ y2 K) p5 nxm0 = (B*\[Gamma]m^\[Epsilon]*
   hm0^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(
3 m* j+ j7 m/ q; B    1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
    hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
      hs0^\[Theta]s)^(1 - \[Epsilon]));
' F0 n/ X  B$ g# L! ?- b* i) Jxs0 = (B*\[Gamma]s^\[Epsilon]*(ps*
; _7 @& C) y- r$ c. _     hs0^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(
    1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
    hm0^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
! n+ Z( n- ^8 x2 k% f6 C' Y$ I; |3 p      hs0^\[Theta]s)^(1 - \[Epsilon]));
Print["\[Eta]_{m,0}=" <> ToString[\[Eta]m0],
", \[Eta]_{s,0}=" <> ToString[\[Eta]s0],
", x_{m,0}=" <> ToString[xm0], ", x_{s,0}=" <> ToString[xs0]]
% h. J. A# x4 l: D, oTT = 100;(* end time *)
1 a4 a8 B) R3 o/ ](* Solve differential equations *)
; E3 l1 d# c' ?( K- [Sol = NDSolve[{xs'[t] = (1 - \[Epsilon])*
4 ~! ~5 V( Z4 ]7 x: R     xs[t]*(   (1 - xs[t]/
# n. F2 r8 S8 e4 w8 Y         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])*
     xm[t]*(   (1 - xm[t]/
          B)*\[Theta]m*\[CurlyPhi]m*(xm[t]/\[Eta]m[t] - 1) -
0 C4 H6 g. P' L& p       xs[t]/B*\[Theta]s*\[CurlyPhi]s*(xs[t]/(ps*\[Eta]s[t]) -
: l/ }6 P  Y$ ~6 q0 b          1) ), \[Eta]m'[
  y  ~. b" T* B( z/ W! P3 {/ i     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],
8 W( ^$ W/ ]7 w+ ~+ @& K. A; i   K'[t] == gRate*K[t], hm[t] == \[Eta]m[t]*K[t],
3 F! M3 W- i; j5 s' R1 ^; Z   hs[t] == \[Eta]s[t]*K[t],
   Sa[t] == (\[Gamma]a^\[Epsilon]*(pa)^(1 - \[Epsilon]))/(\[Gamma]a^\
: a1 A$ x% C# R7 j\[Epsilon]*pa^(1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
4 W3 G, m9 b7 d0 c* M) D       hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
1 Y  g0 n# I) i) R0 _+ k         hs[t]^\[Theta]s)^(1 - \[Epsilon])) + (\[Gamma]m^\[Epsilon]*
      hm[t]^(\[Theta]m*(1 - \[Epsilon]))*pa*
3 U0 h( M- l" l9 n  g- y* i6 X      cap)/((\[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]))*k (t)*
      xm (t)),
0 l$ z& t& v5 T% h0 [" @5 V$ |   Sm[t] == (\[Gamma]m^\[Epsilon]*
% c4 o7 [7 D9 t3 t) [0 u) t) {     hm[t]^(\[Theta]m*(1 - \[Epsilon])))/(\[Gamma]a^\[Epsilon]*pa^(
; T" F  ?" R; b/ O0 t% l! e      1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
4 v0 |: Q) @# m2 I# q$ M: l- v. x      hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
        hs[t]^\[Theta]s)^(1 - \[Epsilon])),
( i3 Q% Q2 n9 C& g4 u   Ss[t] == (\[Gamma]s^\[Epsilon]*(ps*
$ B, \( O; K# S3 V1 b        hs[t]^\[Theta]s)^(1 - \[Epsilon]))/(\[Gamma]a^\[Epsilon]*pa^(
       1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
+ S+ j7 T' \# A/ D& e       hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \[Gamma]s^\[Epsilon]*(ps*
* M3 n0 `6 y$ ?1 r2 J/ x         hs[t]^\[Theta]s)^(1 - \[Epsilon])) - (\[Gamma]m^\[Epsilon]*
& b+ [+ Q( T0 g  f- T7 i! v      hm[t]^(\[Theta]m*(1 - \[Epsilon]))*ps*
" J6 \% U  F& q5 |7 \      csp)/((\[Gamma]a^\[Epsilon]*pa^(
+ F" [& u; E/ s) }) q: z         1 - \[Epsilon]) + \[Gamma]m^\[Epsilon]*
* I: O' w6 \( F9 \: r4 E         hm[t]^(\[Theta]m*(1 - \[Epsilon])) + \
; m8 f7 @2 |0 E/ ~\[Gamma]s^\[Epsilon]*(ps*hs[t]^\[Theta]s)^(1 - \[Epsilon]))*k (t)*
      xm (t)), xm[0] == xm0,
5 N  ?" o2 L" \8 c/ i   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 e: i1 n; l& w! ]- e* ]    0, TT}]
( I9 i$ y, I2 Y* ]1 FPlot[{Evaluate[Sa[t] /. Sol], Evaluate[Sm[t] /. Sol],
  Evaluate[Ss[t] /. Sol]}, {t, 0, TT}, AxesOrigin -> {0, 0},
0 |/ \$ @- {0 l& J PlotRange -> {0., 0.8}, PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]
Plot[{Evaluate[D*Sa[t] /. Sol],
) l9 o3 H# L$ _( _' u* ]' o! w  Evaluate[(D*Sm[t] + (\[Alpha]*(gRate + \[Delta]))/(\[Rho] +
       gRate)) /. Sol], Evaluate[D*Ss[t] /. Sol]}, {t, 0, TT},
$ n8 i/ M5 R% w; b$ I9 P AxesOrigin -> {0, 0}, PlotRange -> {0., 0.8},
% V4 q1 D/ J+ ]0 G, d PlotStyle -> {Blue, Dashed, Dashing[{0.05}]}]
3 F# \6 m/ Z$ i7 u& s. o" J0 k

4 I; S4 M: p! x- U/ Y
' L# p$ h) j" Y. T7 q
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.}.
" ~/ m' @, ?8 R