Variation of number of views of a Youtube video

Question

Is there an established theory that predicts the likely progression of the number of views of a Youtube video ? Or does anyone have an idea how it would go ? Like is there a model function $f_a$ that relates the age $x$ of a video to the number of views, which would depend on a parameter $a$, very hard to measure, evaluating how good the video is ? My idea was : $a \in \mathbb{R}^+$ (or maybe $a$ could take negative values, if a video is clearly offensive or something...) Then $\quad \forall a \quad f_a:\mathbb{R}^+ \rightarrow \mathbb{N}$. Obviously, $f$ is increasing. It puts $0$ onto $0$ and is continuous for $\mathbb{N}$'s induced topology, which just means for any $x\in \mathbb{R}$, the integers of $[0, f(x)]$ are in $f([0,x])$ : $f$ can't skip values, or, two viewers can't watch the video exactly at the same time. Although don't think this observation is of much interest. It also seems reasonable to include exponentials in since the number of new views will depend on the number of views : increasingly at first, until the number of new views per unit time reaches a maximum, then decreasingly (when too many people have seen it they move on). Finally, I would say that when the video is good (i.e. $a$ is high) it reaches its maximum number of new views per unit time earlier than when it's not, because when a video is not too fashionable it has no fashion to go out of. I think it makes sense, in order to keep things fairly simple, to assume that for a substantial part of the video's lifetime the number of Youtube users or the website's popularity does not vary. I don't have much else, and I wondered if there were any notorious statistical models involved in this.