Spreading Processes with Population Heterogeneity Over Multi-Layer Networks

Modeling spreading processes over complex networks has been receiving increasing attention. For example, bond percolation models considering population heterogeneity have been used to derive insights into disease spread and misinformation control. However, most works on spreading processes with population heterogeneity only concentrate on single-layer contact networks. To study how the course of a spreading process changes due to multiple layers of contact networks (e.g., neighborhood vs. schools or Twitter vs. Facebook) while considering population heterogeneity from a principled, mathematical lens, we propose the Multi-layer Mask model based on SIR dynamics. We derive analytical expressions for three fundamental epidemiological quantities: the probability of emergence, the epidemic threshold, and the expected epidemic size. Analytical results are shown to be in near-perfect agreement with the numerical results obtained through extensive simulations. These results reveal the impact of the structure of the multi-layer contact network, viral transmission dynamics, and population heterogeneity on the final state of the spreading process. Thus, they might help develop mitigation and control strategies for disease spread and information diffusion.