Epidemics on contact networks: a general stochastic approach

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.