Synergistic cumulative contagion in epidemic spreading

Most epidemic spreading models assume memoryless agents and independent processes. Nevertheless, many real-life cases are manifestly time-sensitive and show strong correlations. We develop a microscopic description of the infection mechanism that is equipped with memory of past exposures and incorporates the combined effect of multiple infectious sources. Our simulations show a rich variety of phenomena, including loss of universality, collective memory loss, excitability and hysteresis, and indicate that non-Markovian effects significantly alter the properties of dynamical processes in complex networks.