Message passing and moment closure for susceptible-infected-recovered epidemics on finite networks

Robert R. Wilkinson; Kieran J. Sharkey

doi:10.1103/physreve.89.022808

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arXiv · 1309.3661

Message passing and moment closure for susceptible-infected-recovered epidemics on finite networks

Robert R. Wilkinson·Kieran J. Sharkey

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Abstract

The message passing approach of Karrer and Newman [Phys. Rev. E 82, 016101 (2010)] is an exact and practicable representation of susceptible-infected-recovered dynamics on finite trees. Here we show that, assuming Poisson contact processes, a pair-based moment closure representation [Sharkey, J. Math. Biol. 57, 311 (2008)] can be derived from their equations. We extend the applicability of both representations and discuss their relative merits. On arbitrary time-independent networks, as was shown for the message passing formalism, the pair-based moment closure equations also provide a rigorous lower bound on the expected number of susceptibles at all times.

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Robert R. Wilkinson, Kieran J. Sharkey. 2014-02-25. Message passing and moment closure for susceptible-infected-recovered epidemics on finite networks. https://doi.org/10.1103/physreve.89.022808

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