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This paper deals with the statistical signal processing 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 infection dynamics by a deterministic difference equation, thereby yielding a generative model for the infection diffusion. The infection is shown to follow polynomial dynamics and is estimated using an exact nonlinear Bayesian filter. We compute posterior Cramer-Rao bounds to obtain the fundamental limits of the filter that depend on the structure of the network. The SIS model is extended to include homophily, and filtering on these networks is illustrated. Considering the randomly evolving nature of real world networks, a filtering algorithm for estimating the underlying degree distribution is also investigated using generative models for the time evolution of the network. We validate the efficacy of the proposed models and algorithms with synthetic data and Twitter datasets. We find that the SIS model is a satisfactory fit for the information diffusion, and the nonlinear filter effectively tracks the information diffusion.

Tracking Infection Diffusion in Social Networks: Filtering Algorithms and Threshold Bounds