# Fitting 2 curves nonlinearmodelfit

tab1={{0., 1.92308}, {7., 11.5385}, {14., 36.5385}, {21., 75.}, {27.,
123.077}, {35., 300.}, {42., 330.769}}
tab2={{0., 0.}, {7., 3.41463}, {14., 7.80488}, {21., 17.561}, {27.,
32.1951}, {35., 70.7317}, {42., 77.561}}

I want to fit it with the following differential equations. tab1 corresponds to nm[t] and tab2 to ns[t].

I'm using another fit which is the following :

macr = {{0.62, 0.09}, {2.41, 0.27}, {4.02, 0.31}, {5.69,
0.4}, {7.42, 0.8}, {9.16, 1.33}, {10.71, 1.87}, {12.51,
2.76}, {14.25, 3.16}, {15.92, 3.91}, {17.6, 4.76}, {19.34,
5.56}, {28., 16.01}, {42., 17.14}, {56., 19.03}}
lmf = NonlinearModelFit[macr,
c*(1 + Tanh[(x - a)/b]), {{a, 25}, {b, 10}, {c, 7}}, x]
m[x_] = lmf[x + 14]

And here are the differential equations that I want to fit :

sol1 = NDSolve[{ns'[t] ==
alpha*(n[t] - ns[t]*nm[t] )*(m[t] - ns[t])*g[t],
nm'[t] ==
mm*m[t]*(n[t] - ns[t]*nm[t]) +
a*nm[t] + (-b*(nm[t] - nc) - a*nm[t] +
a*nm[t]^(2/3)*(nc^(1/3)))*(Tanh[(nm[t] - nc)*100] + 1),
g'[t] == e*m[t] - h*g[t],
n'[t] == ns'[t]*nm[t] + ns[t]*nm'[t] - d*(n[t] - nm[t]*ns[t]),
g[0] == 0, nm[0] == 0, ns[0] == 0, n[0] == 100}, {n, ns, nm,
g}, {t, 0, 60}]

The initial guess for the parameters I want to fit are the following :

alpha = 0.00005
mm = 0.002
a = 0.2
b = 0.2
d = 0.05
e = 10
f = 0.1
h = 0.01
nc = 222

This guess gives that result (not so great but not so far) :

So just to sum it up, there are 2 elements in my questions :

1. How to fit simultaneously two data

2. How to fit taking into account another unknown function, here $$g[t]$$ and $$n[t]$$.

Thank you in advance