  Models of contagion dynamics, originally developed for infectious diseases,
have proven relevant to the study of information, news, and political opinions
in online social systems. Modelling diffusion processes and predicting viral
information cascades are important problems in network science. Yet, many
studies of information cascades neglect the variation in infectivity across
different pieces of information. Here, we employ early-time observations of
online cascades to estimate the infectivity of distinct pieces of information.
Using simulations and data from real-world Twitter retweets, we demonstrate
that these estimated infectivities can be used to improve predictions about the
virality of an information cascade. Developing our simulations to mimic the
real-world data, we consider the effect of the limited effective time for
transmission of a cascade and demonstrate that a simple model for slow but
non-negligible decay of the infectivity captures the essential properties of
retweet distributions. These results demonstrate the interplay between the
intrinsic infectivity of a tweet and the complex network environment within
which it diffuses, strongly influencing the likelihood of becoming a viral
cascade.
