Exponentially time decaying susceptible-informed (SIT) model for information diffusion process on networks

Modeling information diffusion on networks is a timely topic due to its significance in massive online social media platforms. Models motivated by disease epidemics, such as the Susceptible-Infected-Removed and Susceptible-Infected-Susceptible (SIS), ones have been used for this task, together with threshold models. A key limitation of these models is that the intrinsic time value of information is not accounted for, an important feature for social media applications, since "old" piece of news does not attract adequate attention. We obtain results pertaining to the diffusion size across the diffusion's evolution over time, as well as for early time points that enable us to calculate the phase transition epoch and the epidemic threshold, using mean field approximations. Further, we explicitly calculate the total probability of getting informed for each node depending on its actual path to the single seed node and then propose a novel approach by constructing a Maximum Weight Tree (MWT) to approximate the final fraction of diffusion, with the weight of each node approximating the total probability of getting informed. The MWT approximation is a novel approach that is exact for tree-like network and is specifically designed for sparse networks. It is also fast to compute and provides another general tool for the analyst to obtain accurate approximations of the "epidemic's" size. Extensive comparisons with results based on Monte Carlo simulation of the information diffusion process show that the derived mean field approximations, as well as that employing the MWT one, provide very accurate estimates of the quantities of interest.