  The advent of the era of Big Data has allowed many researchers to dig into
various socio-technical systems, including social media platforms. In
particular, these systems have provided them with certain verifiable means to
look into certain aspects of human behavior. In this work, we are specifically
interested in the behavior of individuals on social media platforms---how they
handle the information they get, and how they share it. We look into Twitter to
understand the dynamics behind the users' posting activities---tweets and
retweets---zooming in on topics that peaked in popularity. Three mechanisms are
considered: endogenous stimuli, exogenous stimuli, and a mechanism that
dictates the decay of interest of the population in a topic. We propose a model
involving two parameters $\eta^\star$ and $\lambda$ describing the tweeting
behaviour of users, which allow us to reconstruct the findings of Lehmann et
al. (2012) on the temporal profiles of popular Twitter hashtags. With this
model, we are able to accurately reproduce the temporal profile of user
engagements on Twitter. Furthermore, we introduce an alternative in classifying
the collective activities on the socio-technical system based on the model.
