  Stochastic processes on complex networks, where each node is in one of
several compartments, and neighboring nodes interact with each other, can be
used to describe a variety of real-world spreading phenomena. However,
computational analysis of such processes is hindered by the enormous size of
their underlying state space.
  In this work, we demonstrate that lumping can be used to reduce any epidemic
model to a Markov Population Model (MPM). Therefore, we propose a novel lumping
scheme based on a partitioning of the nodes. By imposing different types of
counting abstractions, we obtain coarse-grained Markov models with a natural
MPM representation that approximate the original systems. This makes it
possible to transfer the rich pool of approximation techniques developed for
MPMs to the computational analysis of complex networks' dynamics.
  We present numerical examples to investigate the relationship between the
accuracy of the MPMs, the size of the lumped state space, and the type of
counting abstraction.
