Structural diversity effects of multilayer networks on the threshold of interacting epidemics

Foodborne diseases always spread through multiple vectors (e.g. fresh vegetables and fruits) and reveal that multilayer network could spread fatal pathogen with complex interactions. In this paper, first, we use a “top-down analysis framework that depends on only two distributions to describe a random multilayer network with any number of layers. These two distributions are the overlaid degree distribution and the edge-type distribution of the multilayer network. Second, based on the two distributions, we adopt three indicators of multilayer network diversity to measure the correlation between network layers, including network richness, likeness, and evenness. The network richness is the number of layers forming the multilayer network. The network likeness is the degree of different layers sharing the same edge. The network evenness is the variance of the number of edges in every layer. Third, based on a simple epidemic model, we analyze the influence of network diversity on the threshold of interacting epidemics with the coexistence of collaboration and competition. Our work extends the “top-down” analysis framework to deal with the more complex epidemic situation and more diversity indicators and quantifies the trade-off between thresholds of inter-layer collaboration and intra-layer transmission.