  Infection dynamics have been studied extensively on complex networks,
yielding insight into the effects of heterogeneity in contact patterns on
disease spread. Somewhat separately, metapopulations have provided a paradigm
for modeling systems with spatially extended and "patchy" organization. In this
paper we expand on the use of multitype networks for combining these paradigms,
such that simple contagion models can include complexity in the agent
interactions and multiscale structure. We first present a generalization of the
Volz-Miller mean-field approximation for Susceptible-Infected-Recovered (SIR)
dynamics on multitype networks. We then use this technique to study the special
case of epidemic fronts propagating on a one-dimensional lattice of
interconnected networks - representing a simple chain of coupled population
centers - as a necessary first step in understanding how macro-scale disease
spread depends on micro-scale topology. Using the formalism of front
propagation into unstable states, we derive the effective transport
coefficients of the linear spreading: asymptotic speed, characteristic
wavelength, and diffusion coefficient for the leading edge of the pulled
fronts, and analyze their dependence on the underlying graph structure. We also
derive the epidemic threshold for the system and study the front profile for
various network configurations. To our knowledge, this is the first such
application of front propagation concepts to random network models.
