Spreading Processes With Layer-Dependent Population Heterogeneity Over Multilayer Networks

The study of spreading processes on complex networks has gained significant attention recently. For example, bond percolation models considering population heterogeneity have been used to provide insights into disease spread and misinformation control. However, most of these studies focus on single-layer contact networks. In our work, we examine how the spreading process is impacted by the existence of multiple contact network layers, considering layer-dependent population heterogeneity from a principled, mathematical perspective. Using SIR dynamics, we derive expressions for three key epidemiological measures: the probability of emergence, the epidemic threshold, and the expected epidemic size. Through extensive simulations, we demonstrate that our analytical results match the numerical results near-perfectly in the finite node regime. These findings reveal the interplay among the multi-layer network structures, transmission dynamics, and population heterogeneity in determining the final outcome of the spreading process. Furthermore, we investigate the impact of layer-dependent population heterogeneity and identify important factors for developing effective and economical layer-oriented spreading control strategies. Overall, our work provides insights into developing and analyzing mitigation and control strategies for disease spread and information diffusion across multi-layer complex networks.