  Weak ties play a significant role in the structures and the dynamics of
community networks. Based on the susceptible-infected model in contact process,
we study numerically how weak ties influence the predictability of epidemic
dynamics. We first investigate the effects of different kinds of weak ties on
the variabilities of both the arrival time and the prevalence of disease, and
find that the bridgeness with small degree can enhance the predictability of
epidemic spreading. Once weak ties are settled, compared with the variability
of arrival time, the variability of prevalence displays a diametrically opposed
changing trend with both the distance of the initial seed to the bridgeness and
the degree of the initial seed. More specifically, the further distance and the
larger degree of the initial seed can induce the better predictability of
arrival time and the worse predictability of prevalence. Moreover, we discuss
the effects of weak tie number on the epidemic variability. As community
strength becomes very strong, which is caused by the decrease of weak tie
number, the epidemic variability will change dramatically. Compared with the
case of hub seed and random seed, the bridgenss seed can result in the worst
predictability of arrival time and the best predictability of prevalence. These
results show that the variability of arrival time always marks a complete
reversal trend of that of prevalence, which implies it is impossible to predict
epidemic spreading in the early stage of outbreaks accurately.
