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[0]==30000,v2[0]==0,v3[0]==0,v4[0]==0,v5[0]==0,v6[0]==0,v7[0]==0,v8[0]==0,v9[0]==0,v10[0]==0,v11[0]==0,v12[0]==0,v13[0]==0,f[0]==1000000}