Can you be more specific about what the model and parameters are?
From what I understand looking briefly at some online resources, which, based on only superficial skimming, are not very explicit about what parameters are estimated:
My guess is that statsmodels cannot estimate (most of) those models because we don't have a general nonlinear model estimator.
Our main models that are linear in parameters are based on link functions with linear predictor inside, that is
E(y | x) = f(x * beta)
where f maps into a fixed support, R, R+ or [0,1] interval.
For example sigmoid have known supports limits [0, 1] (or [0, n], n known) for fractional or binomial data.
All other models assume that the mean function is linear in parameters.
The best python package for nonlinear least-squares with user provided nonlinear mean function is lmfit.
Josef