This talk (slides) is based on our JASA paper on a hierarchical model of nonhomogeneous Poisson processes (NHPP) for Twitter retweets. The main difference with self-exciting processes for e.g. earthquakes is that we know which original tweet leads to the retweets, and such information is utilised fully in the model, making the likelihood tractable.
Also, this piece of research was done when the platform was still Twitter, not “X, previously known as Twitter”. I wonder if this kind of dynamics still applies these days.