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MathGroup Archive 2007

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Fitting parameters of nonlinear diff equation system

  • To: mathgroup at
  • Subject: [mg81268] Fitting parameters of nonlinear diff equation system
  • From: "Paul Thomas" <paul.pgt at>
  • 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,


{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],
f'[t]==r f[t](1-f[t]/10000000)-h

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