  Albeit epidemic models have evolved into powerful predictive tools for the
spread of diseases and opinions, most assume memoryless agents and independent
transmission channels. We develop an infection mechanism that is endowed with
memory of past exposures and simultaneously incorporates the joint effect of
multiple infectious sources. Analytic equations and simulations of the
susceptible-infected-susceptible model in unstructured substrates reveal the
emergence of an additional phase that separates the usual healthy and endemic
ones. This intermediate phase shows fundamentally distinct characteristics, and
the system exhibits either excitability or an exotic variant of bistability.
Moreover, the transition to endemicity presents hybrid aspects. These features
are the product of an intricate balance between two memory modes and indicate
that non-Markovian effects significantly alter the properties of spreading
processes.
