Epidemic Threshold and Lifetime Distribution for Information Diffusion on Simultaneously Growing Networks

We study information diffusion modeled by epidemic models on a class of growing preferential attachment networks. We show through a thorough simulation study that there is a fundamental difference in the nature of the epidemic process on growing temporal networks in comparison to the same process on static networks. The empirical distribution of the epidemic lifetime on growing networks has a considerably heavier, and possibly infinite, tail. Furthermore, the notion of the epidemic threshold has only minor significance in this context, since network growth reduces the critical value of the corresponding static graph.