Numerical sensitivity analysis of the susceptible- infected- susceptible model on two-layer interconnected networks.

In the field of complex networks, understanding the spreading dynamics in multi-layer networks is crucial for real-world applications such as epidemic control and the analysis of social phenomenon. In this study, a two-layer interconnected network is established, with each layer modeled as a small-world network. To investigate the spreading dynamics on this two-layer network, the classic susceptible-infected-susceptible (SIS) model is applied to it. The governing equations for the Infection proportions on each layer are developed first, followed by the proof of the existence of steady solutions (the proportion of finally infected nodes in the network) and their analytical derivation. Then, the computational model is developed accurately track the time evolution of these solutions using the 4th-order Runge-Kutta method. Finally, a numerical investigation on the influence of parameters is carried out. Three categories of parameters are considered, including inter-layer parameters, intra-layer parameters, and recovery-related parameters. Their effects on the steady solution and the infection velocity of the SIS model on the two-layer networks are summarized. It is found that both inter-layer and intra-layer parameters significantly impact the infection dynamics, an increase in these parameters leads to an increase in the final Infection proportions and a decrease in the time to reach this state. For recovery-related parameters, there exists a maximum value due to the balance of contributions from different aspects. Besides, when the scales of the two layers are unequal, the influence of intra-layer parameters is more obvious for the layer with a smaller scale. The study may contribute to the understanding of spreading dynamics on multi-layer complex networks. It provides practical guidance for managing and controlling the spread of infections in real-world scenarios. The insights gained are valuable for related research and applications in areas like epidemiology and social network analysis.