  Dynamics on networks is considered from the perspective of Markov stochastic
processes. We partially describe the state of the system through network motifs
and infer any missing data using the available information. This versatile
approach is especially well adapted for modelling spreading processes and/or
population dynamics. In particular, the generality of our systematic framework
and the fact that its assumptions are explicitly stated suggests that it could
be used as a common ground for comparing existing epidemics models too complex
for direct comparison, such as agent-based computer simulations. We provide
many examples for the special cases of susceptible-infectious-susceptible (SIS)
and susceptible-infectious-removed (SIR) dynamics (e.g., epidemics propagation)
and we observe multiple situations where accurate results may be obtained at
low computational cost. Our perspective reveals a subtle balance between the
complex requirements of a realistic model and its basic assumptions.
