Journal of Mathematical Biology

, Volume 69, Issue 6–7, pp 1627–1660 | Cite as

Spreading dynamics on complex networks: a general stochastic approach

  • Pierre-André Noël
  • Antoine Allard
  • Laurent Hébert-Dufresne
  • Vincent Marceau
  • Louis J. DubéEmail author


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 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 and susceptible-infectious-removed 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.


Spreading dynamics Complex networks Stochastic processes Contact networks Epidemics Markov processes 

Mathematics Subject Classification (2000)

93A30 05C82 60J28 92D25 92D30 



The research team acknowledges to the Canadian Institutes of Health Research (CIHR), the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Fonds de recherche du Québec—Nature et technologies (FRQ–NT) for financial support. We are grateful to the anonymous referees that have helped improve our presentation.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Pierre-André Noël
    • 1
  • Antoine Allard
    • 2
  • Laurent Hébert-Dufresne
    • 2
  • Vincent Marceau
    • 2
  • Louis J. Dubé
    • 2
    Email author
  1. 1.University of CaliforniaDavisUSA
  2. 2.Département de Physique, de Génie Physique et d’OptiqueUniversité Laval, QuébecQuébecCanada

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