       Fitting parameters of nonlinear diff equation system

• To: mathgroup at smc.vnet.net
• Subject: [mg81268] Fitting parameters of nonlinear diff equation system
• From: "Paul Thomas" <paul.pgt at gmail.com>
• Date: Tue, 18 Sep 2007 00:37:48 -0400 (EDT)

```Hi everyone,

I have a set of differential equations (posted below) that I can solve quite
easily using NDSolve if I define all my parameter values. I have three
parameters that I am currently estimating and would like to try and fit
using actual data I have acquired. The function FindFit though seems to only
work off of a single, non-differential "model" equation. Is this right? Is
there any functionality I can use in Mathematica to help me fit the
parameters of a system like this? Right now I am using the "Table" function
to solve the equation using NDSolve over a range for the parameters. The
problem is that I have the multiple parameters that I'd like to fit so it's
quickly become an enormously tedious set of solutions (as I have to a range
of each parameter at a range of the other two parameters).

Here's one of the sets I've been trying to do this with: The parameters I'd
be solving for include b1, r, and h. Like I said, I can make good estimates
of these and I know ranges, but I'd like to do a proper fit so that I can
quantify sensitivity etc. Thanks,

Paul

{v1'[t]==-b1 v1[t] f[t],
v2'[t]==2 b1 f[t] v1[t]-b1 f[t] v2[t],
v3'[t]==2 b1 f[t] v2[t]-b1 f[t] v3[t],
v4'[t]==2 b1 f[t] v3[t]-b1 f[t] v4[t],
v5'[t]==2b1 f[t]v4[t]-v5[t],
v6'[t]==2v5[t]-v6[t],
v7'[t]==2v6[t]-v7[t],
v8'[t]==2v7[t]-v8[t],
v9'[t]==2v8[t]-v9[t],
v10'[t]==2v9[t]-v10[t],
v11'[t]==2v10[t]-v11[t],
v12'[t]==2v11[t]-v12[t],
v13'[t]==2v12[t],
f'[t]==r f[t](1-f[t]/10000000)-h
(v1[t]+v2[t]+v3[t]+v4[t]+v5[t]+v6[t]+v7[t]+v8[t]+v9[t]+v10[t]+v11[t]+v12[t]+v13[t])
f[t],
v1==30000,v2==0,v3==0,v4==0,v5==0,v6==0,v7==0,v8==0,v9==0,v10==0,v11==0,v12==0,v13==0,f==1000000}

```

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