Hi, me and @stemangiola solved a similar problem, you may find it useful to check out our reparametrization of the sigmoid function: Difficulties with logistic population growth model
I didn’t check the math very carefully, but it seems to me that the only (but possibly important) difference is that we have a parameter for “value of the sigmoid at midpoint of the data” instead of “maximal value of the sigmoid”. (the paper we speak about in the linked post is still in the publication purgatory, I’ll ask @stemangiola whether we could make a preprint available)
Also note, that you can use triple backticks to format chunks of code/program output/… I’ve edited the first post for you, you might want to edit the rest of the thread :-)
Hope that helps!