  We build a model of information cascades on feed-based networks, taking into
account the finite attention span of users, message generation rates and
message forwarding rates. Using this model, we study through simulations, the
effect of the extent of user attention on the probability that the cascade
becomes viral. In analogy with a branching process, we estimate the branching
factor associated with the cascade process for different attention spans and
different forwarding probabilities, and demonstrate that beyond a certain
attention span, critical forwarding probabilities exist that constitute a
threshold after which cascades can become viral. The critical forwarding
probabilities have an inverse relationship with the attention span. Next, we
develop a semi-analytical approach for our model, that allows us determine the
branching factor for given values of message generation rates, message
forwarding rates and attention spans. The branching factors obtained using this
analytical approach show good agreement with those obtained through
simulations. Finally, we analyze an event specific dataset obtained from
Twitter, and show that estimated branching factors correlate well with the
cascade size distributions associated with distinct hashtags.
