Epidemic fronts in complex networks with metapopulation structure.
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. Using a generalization of the Miller-Volz mean-field approximation for susceptible-infected-recovered (SIR) dynamics on multitype networks, we 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 macroscale disease spread depends on microscale topology. Applying 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.