title: Message passing and moment closure for susceptible-infected-recovered epidemics on finite networks.
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.
authors.affiliation: The University of Liverpool, Liverpool, United Kingdom.
authors.forename: Robert R
authors.initials: RR
authors.lastname: Wilkinson
authors.affiliation: The University of Liverpool, Liverpool, United Kingdom.
authors.forename: Kieran J
authors.initials: KJ
authors.lastname: Sharkey
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology*; D003198:Computer Simulation; D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D004198:Disease Susceptibility / Q000453:epidemiology*; D006801:Humans; D015233:Models, Statistical; D015995:Prevalence; D018570:Risk Assessment; D013269:Stochastic Processes