  Online social networks represent a main source of communication and
information exchange in today's life. They facilitate exquisitely news sharing,
knowledge elicitation, and forming groups of same interests. Researchers in the
last two decades studied the growth dynamics of the online social networks
extensively questing a clear understanding of the behavior of humans in online
social networks that helps in many directions, like engineering better
recommendation systems and attracting new members. However, not all of social
networks achieved the desired growth, for example, online social networks like
MySpace, Orkut, and Friendster are out of service today. In this work, we
present a probabilistic theoretical model that captures the dynamics of the
social decay due to the inactivity of the members of a social network. The
model is proved to have some interesting mathematical properties, namely
\textit{submodularity}, which imply achieving the model optimization in a
reasonable performance. That means the maximization problem can be approximated
within a factor of $(1-1/e)$ and the minimization problem can be achieved in
polynomial time.
