bootstrap for nonlinear regression on nonnegative data

I am trying to fit a (relatively complicated differential equation
based) model to some time series data. The model has several
parameters that need to be determined, and I'd like to get confidence
intervals on these parameters. This seems to call for some sort of
bootstrap procedure to generate surrogate time series from resampled
residuals, but there's a catch. Both the data and the model
predictions must be positive. Is there a good way to do this? Or a
good reference that's accessible to a non-statistician that might help
me out?

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