Diversity of multilayer networks and its impact on collaborating epidemics

Interacting epidemics on diverse multilayer networks are increasingly important in modeling and analyzing the diffusion processes of real complex systems. A viral agent spreading on one layer of a multilayer network can interact with its counterparts by promoting (cooperative interaction), suppressing (competitive interaction), or inducing (collaborating interaction) its diffusion on other layers. Collaborating interaction displays different patterns: (i) random collaboration, where intralayer or interlayer induction has the same probability; (ii) concentrating collaboration, where consecutive intralayer induction is guaranteed with a probability of 1; and (iii) cascading collaboration, where consecutive intralayer induction is banned with a probability of 0. In this paper, we develop a top-bottom framework that uses only two distributions, the overlaid degree distribution and edge-type distribution, to model collaborating epidemics on multilayer networks. We then state the response of three collaborating patterns to structural diversity (evenness and difference of network layers). For viral agents with small transmissibility, we find that random collaboration is more effective in networks with higher diversity (high evenness and difference), while the concentrating pattern is more suitable in uneven networks. Interestingly, the cascading pattern requires a network with moderate difference and high evenness, and the moderately uneven coupling of multiple network layers can effectively increase robustness to resist cascading failure. With large transmissibility, however, we find that all collaborating patterns are more effective in high-diversity networks. Our work provides a systemic analysis of collaborating epidemics on multilayer networks. The results enhance our understanding of biotic and informative diffusion through multiple vectors.