Mean-field modeling approach for understanding epidemic dynamics in interconnected networks

Modern systems (e.g., social, communicant, biological networks) are increasingly interconnected each other formed as ‘networks of networks’. Such complex systems usually possess inconsistent topologies and permit agents distributed in different subnetworks to interact directly/indirectly. Corresponding dynamics phenomena, such as the transmission of information, power, computer virus and disease, would exhibit complicated and heterogeneous tempo-spatial patterns. In this paper, we focus on the scenario of epidemic spreading in interconnected networks. We intend to provide a typical mean-field modeling framework to describe the time-evolution dynamics, and offer some mathematical skills to study the spreading threshold and the global stability of the model. Integrating the research with numerical analysis, we are able to quantify the effects of networks structure and epidemiology parameters on the transmission dynamics. Interestingly, we find that the diffusion transition in the whole network is governed by a unique threshold, which mainly depends on the most heterogenous connection patterns of network substructures. Further, the dynamics is highly sensitive to the critical values of cross infectivity with switchable phases.