Epidemic fronts in complex networks with metapopulation structure

TL;DR

This paper extends epidemic modeling on complex multitype networks by analyzing how disease fronts propagate in interconnected network structures, deriving key parameters like speed and thresholds, and applying front propagation theory to random networks.

Contribution

It generalizes the mean-field approximation for SIR dynamics on multitype networks and introduces a novel analysis of epidemic front propagation on network lattices.

Findings

Derived the asymptotic speed and wavelength of epidemic fronts.

Established the epidemic threshold for multitype network systems.

Analyzed how network topology influences disease spread dynamics.

Abstract

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.