Piet Van Mieghem (Professor, Delft University of Technology; Chair, Network Architectures and Services (NAS))
Abstract. We concentrate on the simple SIS epidemics on any network. First, general (exact) properties are derived, followed by a mean-field approximation that culminates in the N-intertwined approximation (NIMFA). Several extensions and attractive features of NIFMA are presented.
Since there does not exist an SIS epidemic threshold in finite networks (due to the absorbing state in the SIS Markov chain), we propose two other approaches to "define" the meta-stable state and corresponding epidemic threshold, which resembles the epidemic behavior observed in realistic epidemics (and simulations). We elaborate on the epsilon-SIS model, where, in addition to an infection rate beta and a curing rate delta, each node possesses a self-infection rate epsilon. Exact results on the complete graph and the star graph are presented.
Finally, we extend the Markovian SIS model to general infection times. Twitter measurements indicate that the re-tweet times (corresponding to infection times) are heavy-tailed (and very close to a lognormal distribution).