  The 21st century has redefined the way we communicate, our concept of
individual and group privacy, and the dynamics of acceptable behavioral norms.
The messaging dynamics on Twitter, an internet social network, has opened new
ways/modes of spreading information. As a result cyberbullying or in general,
the spread of offensive messages, is a prevalent problem. The aim of this
report is to identify and evaluate conditions that would dampen the role of
cyberbullying dynamics on Twitter. We present a discrete-time non-linear
compartmental model to explore how the introduction of a Quarantine class may
help to hinder the spread of offensive messages. We based the parameters of
this model on recent Twitter data related to a topic that communities would
deem most offensive, and found that for Twitter a level of quarantine can
always be achieved that will immediately suppress the spread of offensive
messages, and that this level of quarantine is independent of the number of
offenders spreading the message. We hope that the analysis of this dynamic
model will shed some insights into the viability of new models of methods for
reducing cyberbullying in public social networks.
