Spreading dynamics on complex networks: a general stochastic approach

Journal of Mathematical Biology
Pierre-André NoëlLouis J Dubé

Abstract

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.

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Citations

Jul 22, 2015·Proceedings of the National Academy of Sciences of the United States of America·Laurent Hébert-Dufresne, Benjamin M Althouse
Aug 8, 2014·Journal of the Royal Society, Interface·Benjamin M Althouse, Laurent Hébert-Dufresne
May 3, 2019·Scientific Reports·Clara StegehuisJohan S H van Leeuwaarden

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