Solve the ODE with NDSolve and dependet variables - wolfram-mathematica

Question

I have intialconditions:
sf = 200;
sm = 100;
p = 40;
betaf = 0.15;
betam = 0.15;
mums = 0.02;
mufs = 0.02;
sigma = 0.20;
mum = 0.02;
muf = 0.02;
and the ODE:
sf' := -muf*sf + (betaf + mums + sigma)*p - HarmonicMean[sf, sm];
sm' := -mum*sm + (betam + mufs + sigma)*p - HarmonicMean[sf, sm}];
p' := p - (mufs + mums + sigma)*p + HarmonicMean[{sf, sm}];
That i want is an abstract solution (sf(t),sm(t),p(t)) with NDSolve to plot it later.
My problem is that all variables are dependet in all 3 equations, so i don't know how to write the NDSolve call.

Answer 1

I could not manage to get an analytic solution, but the numerical one goes like this. Note that not all symbols you listed are variables of the system: those not being dependent of the independent variable t are parameters. (Also note that there are some typos in the OP's code).
variables = {sf[t], sm[t], p[t]};
parameters = {betaf -> 0.15, betam -> 0.15, mums -> 0.02,
mufs -> 0.02, sigma -> 0.20, mum -> 0.02, muf -> 0.02};
equations = {
sf'[t] == -muf*sf[t] + (betaf + mums + sigma)*p[t] -
HarmonicMean[{sf[t], sm[t]}],
sm'[t] == -mum*sm[t] + (betam + mufs + sigma)*p[t] -
HarmonicMean[{sf[t], sm[t]}],
p'[t] ==
p[t] - (mufs + mums + sigma)*p[t] + HarmonicMean[{sf[t], sm[t]}],
sf[0] == 200,
sm[0] == 100,
p[0] == 40
};
sol = NDSolve[equations /. parameters, variables, {t, 0, 100}];
Plot[Evaluate[variables /. sol], {t, 0, 100}]