  We analyze the Bass and SI models for the spreading of innovations and
epidemics, respectively, on homogeneous complete networks, circular networks,
and heterogeneous complete networks with two homogeneous groups. We allow the
network parameters to be time dependent, which is a prerequisite for the
analysis of optimal strategies on networks. Using a novel top-down analysis of
the master equations, we present a simple proof for the monotone convergence of
these models to their respective infinite-population limits. This leads to
explicit expressions for the expected adoption or infection level in the Bass
and SI models, respectively, on infinite homogeneous complete and circular
networks, and on heterogeneous complete networks with two homogeneous groups
with time-dependent parameters.
