Dynamic message-passing equations and applications to epidemic and information spreading on networks
Andrey Lokhov, LPTMS
Understanding and quantifying the out-of-equilibrium dynamics is one of the major tasks of today’s science. Using dynamic cavity method on time trajectories, we show how to derive dynamic message-passing (DMP) equations for a large class of models with irreversible dynamics – the key point that makes the problem solvable. These equations are asymptotically exact for locally tree-like graphs and generally provide a good approximation for real-world networks. We illustrate the approach by applying the DMP equations for susceptible-infected-recovered (SIR) and ignorant-spreader-stifler models (ISS) models to the problems of inference of epidemic origin and optimal information spreading with awareness.