Effects of weak ties on epidemic predictability on community networks

Weak ties play a significant role in the structures and the dynamics of community networks. Based on the contact process, we study numerically how weak ties influence the predictability of epidemic dynamics. We first investigate the effects of the degree of bridge nodes on the variabilities of both the arrival time and the prevalence of disease, and find out that the bridge node with a small degree can enhance the predictability of epidemic spreading. Once weak ties are settled, the variability of the prevalence will display a complete opposite trend to that of the arrival time, as the distance from the initial seed to the bridge node or the degree of the initial seed increases. More specifically, the further distance and the larger degree of the initial seed can induce the better predictability of the arrival time and the worse predictability of the prevalence. Moreover, we discuss the effects of the number of weak ties on the epidemic variability. As the community strength becomes very strong, which is caused by the decrease of the number of weak ties, the epidemic variability will change dramatically. Compared with the case of the hub seed and the random seed, the bridge seed can result in the worst predictability of the arrival time and the best predictability of the prevalence.