  In this work we introduce a model based on master equations to describe the
time evolution of the popularity of topics and hashtags on the Twitter social
network. Specifically, we model the number of times a certain hashtag appears
on the network as a function of time. In our model, the behavior of this
quantity depends on the degree distribution of the network and the extrinsic
interest the community has for the topic or hashtag. From the master equation,
we are able to obtain explicit solutions for the mean and variance. We propose
a gamma kernel function to model the topic popularity, which is quite simple
and yields reasonable results. Finally, we validate the plausibility of the
model by analyzing actual Twitter data obtained through the public API.
