  We prove that, for Poisson transmission and recovery processes, the classic
Susceptible $\to$ Infected $\to$ Recovered (SIR) epidemic model of Kermack and
McKendrick provides, for any given time $t>0$, a strict lower bound on the
expected number of suscpetibles and a strict upper bound on the expected number
of recoveries in the general stochastic SIR epidemic. The proof is based on the
recent message passing representation of SIR epidemics applied to a complete
graph.
