If you didn't get this solved. I have done parameter estimation with models defined by ODE's where negative solutions are a problem and one can only avoid them with great difficulty if the standard explicit methods for solving the ODE are used. I found that using implicit methods could be a great help.
For example in the exponential case dN/dt = -k*N the simple finite difference approximation is N_{t+1}-N+t -------------- = -k*N_t , k>=0 h or N_{t+1} = N_t -k*h*N_t and if k*h gets too large N_{t+1} goes negative and you are in trouble. Consider instead the implicit formulation where the second N_t on the RHS is replaced by N_{t+1} and one gets N_{t+1} = N_t/(1+k*h) which is correct for k*h=0 and as k*h--> infinity For a more complicated example see http://otter-rsch.com/admodel/cc4.html for something I called "semi-implicit". I hope these ideas will be useful for your problem. Cheers, Dave -- David A. Fournier P.O. Box 2040, Sidney, B.C. V8l 3S3 Canada Phone/FAX 250-655-3364 http://otter-rsch.com ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.