  We analyze the late-time relaxation dynamics for a general contagion model.
In this model, nodes are either active or failed. Active nodes can fail either
"spontaneously" at any time or "externally" if their neighborhoods are
sufficiently damaged. Failed nodes may always recover spontaneously. At late
times, the breaking of time-translation-invariance is a necessary condition for
physical aging. We observe that time-translational invariance is lost for
initial conditions that lie between the basins of attraction of the model's two
stable stationary states. Based on corresponding mean-field predictions, we
characterize the observed model behavior in terms of a phase diagram spanned by
the fractions of spontaneously and externally failed nodes. For the square
lattice, the phases in which the dynamics approaches one of the two stable
stationary states are not linearly separable due to spatial correlation
effects. Our results provide new insights into aging and relaxation phenomena
that are observable in a model of social contagion processes.
