Epidemic process on partially overlapped multi-layer networks

The phenomenon of epidemic spread has received continuous attention due to its profound applications in a wide range of social and economic activities. In this paper we propose a partially overlapped multi-layer network model and illustrate the influence of multi-layer structure on outbreaks. Combined with the classic SIS model, we propose a set of discrete Markov equations and make first-order approximation on the threshold of epidemic outbreak. In comparison with independent simplex networks, we find that a multi-layer structure promotes epidemic spread and leads to a smaller critical threshold. In addition, we also find that the epidemic process on partially overlapped multi-layer networks is dominated by the layer with the largest main eigenvalue. Through Monte Carlo simulations, we find that the role of the dominant layer is irrelevant with its size, which means a small set of nodes can exhibit a disproportionate impact on the epidemics of a large network. Our research sheds light on the epidemic process on partially overlapped multi-layer complex systems, and provides a theoretical explanation of unexpected real-world outbreaks.