  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.
