Study Of Epidemic Spreading With SIR Model In Interdependent Networks

Networks exist widely in the real world. The morphology and structure of the network have been evolving with the complex relationship between the nodes, and the interaction of various factors in the networks. There exist a large number of dynamical processes in complex network-s, such as various spreading processes, cascading failures, and synchronization. The spread of the epidemic is a widely existing dynamical process in the network which includes the spread of biochemical disease, computer virus, information, cultural norms, and rumor. Meanwhile, it has been discovered that networks in the real world are not isolated, but often couple with each other according to various rules. In this paper, by considering the scenario that communication networks and infrastructure networks are often interdependent with each other, we study the spread of epi-demic with SIR (susceptible-infected-removed/recovered) model in interdependent networks from the following aspects:(1) We propose a model based on epidemiological SIR model to study the epidemic spread-ing in interdependent networks. Study of interdependent networks has become a research hotspot in complex networks in recent years. The present researches on interdependent networks mainly focus on the analysis of robustness with the removal of nodes. In reality, interdependent net-works are facing a variety of threats, such as the infection of epidemic. But at present there is no dependence study of epidemic spreading in interdependent networks. Therefore, we combine the interdependent networks model and SIR epidemic model, and take the lead in the research of epidemic spreading in interdependent networks. We propose a theoretical solution to get the proportions of removed nodes and failed nodes in degree-degree uncorrelated networks using the percolation theory and the mean-field theory, and reveal that there exist two critical points of the proportion of removed and failed nodes by changing of effective spreading rate. Moreover, we also find that the robustness to the spread of epidemic in interdependent networks is worse than that in single network. With the increase of average degree, the robustness to the spread of epidemic in interdependent networks get worse, which is different from previous researches. (2) Furthermore, we study the epidemic spreading in interdependent networks from the views of different network structures, coupling strengths, and inter degree-degree correlations. We ex-plore the spreading of epidemic with SIR model not only in typical interdependent networks, but also in interdependent networks with different network structures, coupling strengths, and inter degree-degree correlations. In this aspect, we improve and complement the research of epidemic spreading in interdependent networks under a more realistic situation. The results of the study show that:epidemic is inhibited when there is strong spatial structure in networks, the robustness to the spread of epidemic in interdependent networks get better when increasing the average degree of coupling links or coupling with assortative links. These results are instructive for improving the robustness of interdependent networks with realistic scenarios.(3) We study the epidemic spreading in interdependent networks when the load and capacity of nodes are considered. Epidemic spreading and overloaded cascading failures are extensively investigated in the researches of complex networks. Traditionally, these two dynamics correspond to independent topics in the researches of complex networks. But in practice, they interact with each other and neither of their effects can be ignored in many real cases. We combine a model based on epidemiological SIR model with a local load sharing cascading failures model to explore the dynamical interaction among epidemic spreading, cascading overload, and cascading failures in interdependent networks using the percolation theory and the mean-field theory. We observe a new phenomena that with a high infectivity, a large number of active nodes survive only if the tolerance parameter within some interval. Through qualitative and quantitative analysis, we also find that the most proportion of active nodes survive when the networks are coupled with assortative links. These unconventional phenomenons with this model provide us a new understanding of the dynamical processes in interdependent networks:in the scenarios of two negative dynamical processes interacting with each other, the results can be positive under certain conditions and the robustness of system can be improved.