Modeling Multi-state Diffusion Process in Complex Networks: Theory and Applications

There is a growing interest to understand the fundamental principles of how epidemic, ideas or information spread over large networks (e.g., the Internet or online social networks). Conventional approach is to use SIS models (or its derivatives). However, these models usually are over-simplified and may not be applicable in realistic situations. In this paper, we propose a generalization of the SIS model by allowing intermediate states between susceptible and infected states. To analyze the diffusion process on large graphs, we use the ``mean-field analysis technique'' to determine which initial condition leads to or prevents information or virus outbreak. Numerical results show our methodology can accurately predict the behavior of the phase-transition process for various large graphs (e.g., complete graphs, random graphs or power-law graphs). We also extend our generalized SIS model to consider the interaction of two competing sources (i.e., competing products or virus-antidote modeling). We present the analytical derivation and show experimentally how different factors, i.e., transmission rates, recovery rates, number of states or initial condition, can affect the phase transition process and the final equilibrium. Our models and methodology can serve as an essential tool in understanding information diffusion in large networks.