Imagine new product hitting the market, sales dynamically rise, achieve plateau, and then steadily drop. I'm thinking of something with dynamics that when depicted on a plot (counts over time), will resemble Little Prince's drawing of snake who ate an elephant (well, maybe with less extreme drop at the end).
What would be the best model for such process? I imagine I could find some interesting hints in epidemiological models -- if yes, could you suggest something? I'm looking for something relatively simple, using just counts over time as data.