Contagion Spreading on Complex Networks: Fitness-Based Local Dynamics

We propose and study a model of spreading which takes into account the strength or quality of contagions as well as the local dynamics occurring at various nodes. The model exhibits quality-dependent exponential time scales at early times leading to a slowly evolving quasi-stationary state. We also investigate the activity of nodes and find a power-law distribution with a robust exponent independent of network topology. Our results are consistent with recent empirical observations.