  It is common to use a compartmental, fluid model described by a system of
ordinary differential equations (ODEs) to model disease spread. In addition to
their simplicity, these models are also the mean-field approximations of more
accurate stochastic models of disease spread on contact networks. For the
simplest case of a stochastic susceptible-infected-susceptible (SIS) process
(infection with recovery) on a complete network, it has been shown that the
fraction of infected nodes converges to the mean-field ODE as the number of
nodes increases. However the proofs are not simple, requiring sophisticated
probability, partial differential equations (PDE), or infinite systems of ODEs.
We provide a short proof in this case for convergence in mean-square on finite
time-intervals using a system of two ODEs and a moment inequality and also
obtain the first lower bound on the expected fraction of infected nodes.
