Synergistic cumulative contagion in epidemic spreading

Most epidemic spreading models assume memoryless agents and independent transmissions along different infection channels. Nevertheless, many real-life cases are manifestly time-sensitive and show strong correlations. Although some recent research efforts have analyzed the effects of memory and others have explored synergistic contagion schemes, both topics are rarely combined. We develop a microscopic description of the infection mechanism that is endowed with memory of past exposures and simultaneously incorporates the joint effect of multiple infectious sources. Already in unstructured substrates our simulations show a rich variety of phenomena, including loss of universality, collective memory loss, bistability, hysteresis and excitability. These features are the product of an intricate balance between two memory modes and indicate that non-Markovian effects significantly alter the properties of contagion and spreading processes. The future inclusion of heterogeneous contact networks and more elaborate modeling details will provide additional insight on the relevance of microscopic mechanisms and topological properties regarding dynamical processes in complex networks.