  We apply the cavity master equation (CME) approach to epidemics models. We
explore mostly the susceptible-infectious-susceptible (SIS) model, which can be
readily treated with the CME as a two-state. We show that this approach is more
accurate than individual based and pair based mean field methods, and a
previously published dynamic message passing scheme. We explore average case
predictions and extend the cavity master equation to SIR and SIRS models.
