  Spreading phenomena are ubiquitous in nature and society. For example,
disease, rumor, and information spread over underlying social and information
networks. It is well known that there is no threshold for epidemic models on
scale-free networks; this suggests that disease can spread on such networks,
regardless of how low the contact rate may be. In this paper, I consider six
models with different contact and propagation mechanisms. Each model is
analyzed by degree-based mean-field theory. I show that the presence or absence
of an outbreak threshold depends on the contact and propagation mechanism.
