  This paper deals with the statistical signal pro- cessing over graphs for
tracking infection diffusion in social networks. Infection (or Information)
diffusion is modeled using the Susceptible-Infected-Susceptible (SIS) model.
Mean field approximation is employed to approximate the discrete valued
infected degree distribution evolution by a deterministic ordinary differential
equation for obtaining a generative model for the infection diffusion. The
infected degree distribution is shown to follow polynomial dynamics and is
estimated using an exact non- linear Bayesian filter. We compute posterior
Cramer-Rao bounds to obtain the fundamental limits of the filter which depend
on the structure of the network. Considering the time-varying nature of the
real world networks, the relationship between the diffusion thresholds and the
degree distribution is investigated using generative models for real world
networks. In addition, we validate the efficacy of our method with the
diffusion data from a real-world online social system, Twitter. We find that
SIS model is a good fit for the information diffusion and the non-linear filter
effectively tracks the information diffusion.
