A node-based SIRS epidemic model on two-layer interconnected networks: Dynamical analysis of interplay between layers

From the micro-level perspective of individuals, this paper proposes a node-based SIRS epidemic model on two-layer networks, and investigates the stability of the equilibrium in the model as well as the influence of network structures and infected or recovered rate on disease propagation. By using the stability theory, we give the accurate sufficient condition for the stability as well as the threshold of disease prevalence, showing the threshold of such two-layer network is less than that of isolated single -layer network. Also, an easy-to-use approximate criterion for stability of disease-free equilibrium is provided for the two-layer network with general intra-layer structures when the infected rate across layers is far less than that within layers. Further, extensive numerical simulations on several classical network structure models verify the theoretical results, and show some new interesting results: (1) for the duplex network with equivalent number of connections each layer, the infected rate across layers has more significant effect on epidemic spreading than that within layers; (2) when fixing the whole network edge density, the same number of connections each layer always be the most conductive to propagate of the disease for the duplex network of ER structures, but it is the most/worst conductive to propagate at large/small infected rate for the duplex network of small -world structures.