[atoav]

I mean humanity is a little bit more complex than bacteria growth, for example because humans can to some degree influence if, when and how many kids they are getting.

But the logistic growth function is used to model populations in animals as well. So the question is what is your counteragrument?

1. reality is more complex than the logistic function, but ultimately in fact we would reach some sort of saturation effect, e.g. by humanity moderating the birth rates.

2. reality is more complex, but infinite growth in an finite habitat is somehow possible (note, that infinity is a huge number)

If it is the latter I'd be very curious to see your mathematical model and your reasoning behind it.

On the topic of model complexity: the logistic growth function is a simplification and in reality one would have to incorporate at all kind of resources (and their geographical locations, renewing rates, etc) in a complex mega model. But I do not see how any model could sustain infinite humans. And if it can't it means there is saturation and that means the logistic growth function is a good mental approximation for populations.

Also see: https://bio.libretexts.org/Bookshelves/Introductory_and_Gene...