  Stochastic processes can model many emerging phenomena on networks, like the
spread of computer viruses, rumors, or infectious diseases. Understanding the
dynamics of such stochastic spreading processes is therefore of fundamental
interest. In this work we consider the wide-spread compartment model where each
node is in one of several states (or compartments). Nodes change their state
randomly after an exponentially distributed waiting time and according to a
given set of rules. For networks of realistic size, even the generation of only
a single stochastic trajectory of a spreading process is computationally very
expensive.
  Here, we propose a novel simulation approach, which combines the advantages
of event-based simulation and rejection sampling. Our method outperforms
state-of-the-art methods in terms of absolute run-time and scales significantly
better, while being statistically equivalent.
