  This paper studies a novel approach for approximating the behavior of
compartmental spreading processes. In contrast to prior work, the methods
developed describe a dynamics which bound the exact moment dynamics, without
explicitly requiring a priori knowledge of non-negative (or non-positive)
covariance between pairs of system variables. Moreover, we provide systems
which provide both upper- and lower- bounds on the process moments. We then
show that when system variables are shown to be non-negatively (or
non-positively) correlated for all time in the system's evolution, we may
leverage the knowledge to create better approximating systems. We then apply
the technique to several previously studied compartmental spreading processes,
and compare the bounding systems' performance to the standard approximations
studied in prior literature.
