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)PLEEE81539-375510.1103/PhysRevE.82.016101] 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)10.1007/s00285-008-0161-7] 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. © 2014 Published by the American Physical Society.