# [R] Fitting data with optim or nls--different time scales

Leslie Chavez leslou at ctbp.ucsd.edu
Tue Aug 8 20:22:06 CEST 2006

```Hi,

I have a system of ODE's I can solve with lsoda.

Model=function(t,x,parms)
{
#parameter definitions
lambda=parms; beta=parms;
d = parms; delta = parms;
p=parms;    c=parms

xdot = lambda - (d*x)- (beta*x*x)
xdot = (beta*x*x) - (delta*x)
xdot = (p*x) - (c*x)

return(list(xdot))
}

I want to fit the output out[,4] to experimental data that is only
available on days 0, 7, 12, 14, 17, and 20. I don't know how to set up
optim or nls so that it takes out[,4] on the appropriate day, but still
runs lsoda on a time scale of 0.01 day.

Below is the function I've been using to run 'optim', at the
course-grained time scale:

Modelfit=function(s) {
parms[1:4]=s[1:4]; times=c(0,7,12,14,17,20,25)
out=lsoda(x0,times,Model,parms)
mse=mean((log10(out[,4])-log10(i(times)))^2)
#	cat(times)
return(mse)
}
#x0=c(T0,I0,V0)
x0=c(2249,0,1)
#parms(lambda, beta, d, delta, p, c)
parms[5:6]=c(1.0,23)

s0=c(49994,8456,6.16E-8,0.012) #initial values

fit=optim(s0,Modelfit)

Right now, lsoda is being run on too course-grained a time scale in the
function Modelfit. Most examples of optim and nls I have found compare
two data sets at the same times, and run lsoda on the time scale the
data is available at, but I would like to run lsoda at a finer scale, and
only compare the appropriate time points with the experiment.  I have also
tried using nls, but I have the same problem. Does anyone have
suggestions?

Thank you very much,

Leslie

```