I would be very grateful if anyone could help with manipulating the solution to the system of differential equations below. I've tried just about everything I can think of all to no avail. The code doesn't seem to be working (i.e. the parameters I'm trying to adjust have no effect on the dynamics of the graphs which can't be right-I computed other values myself and it gave a different plot). I have had a look at some similar topics like Manipulate a Differential Equation result but its quite specific for single differential equations rather than a system of equations. The variables I'd like to vary are mhigh, s0, p0 and z0.
My code is given below:
Needs["PlotLegends`"];
De = 2.1;
B = 2.3;
B2 = 0.001;
mhigh = 0.001, mlow = 0.0004;
fr = 0.77, fs = 1, fp = 1.4;
s0 = 1000;
z0 = 1000;
p0 = 0;
r0 = 0;
solutionN2 =
NDSolve[{
Z'[t] == De*(S[t] + P[t] + R[t]) - B*Z[t]*((fs*S[t]) + (fp*P[t]) + (fr*R[t])),
S'[t] == fs*B* S[t]*Z[t] - (mlow + mhigh)*S[t] - De *S[t],
P'[t] == fp* B* P[t]*Z[t] + mlow *S[t] - B2* P[t] - De* P[t],
R'[t] == fr *B* R[t]*Z[t] + mhigh* S[t] + B2 *P[t] - De *R[t],
S[0] == s0, P[0] == p0,
R[0] == r0, Z[0] == z0},
{S, P, R, Z}, {t, 0, 200}];
Manipulate[
Plot[{Z[t] /. solutionN2, S[t] /. solutionN2, P[t] /. solutionN2, R[t] /. solutionN2},
{t, 0, 200},
ImageSize -> {700},
PlotStyle -> {Brown, Red, Blue, Darker[Green]},
PlotLegend -> {"Z", "S", "P", "R"}, LegendPosition -> {0.2, -0.2},
FrameLabel -> {Style["time (in days)", Medium]}],
{{s0, 1000, s0:initial sus pop"}, 0, 5000,
ImageSize -> {Tiny}, Appearance -> "Labeled"},
{{z0, 0, z0:initial resources"}, 0, 5000,
ImageSize -> {Tiny}, Appearance -> "Labeled"},
{{p0, 0, p0:initial p. sus. pop"}, 0, 1000,
ImageSize -> {Tiny}, Appearance -> "Labeled"},
{{mhigh, (0.001), "mut. rate"}, 0, 0.01,
ImageSize -> {Tiny}, Appearance -> "Labeled"}]
Please bear with me as I'm a beginner with Mathematica. As stated, any useful help would be so much appreciated as Ive spent nearly the whole day trying to sort this out.