Research On Spread Model And Dynamics Of Two-layers Coupled Network

Many complex systems have nodes with a variety of different functions,in which the nodes are connected to form a multilayer networks.The spread of epidemic on top of multilayer networks has become an important research topic in the field of complex networks.At present,it is lack of corresponding theoretical analysis to two questions of how the multilayer networks structure affects the spread dynamics and what the differences of the spread processes between multilayer networks and the corresponding isolated networks are.In this dissertation,in order to reflect the process of epidemic spreading,we focus on constructing multilayer coupled network propagation model by using mean-field approach,nonlinear differential dynamics theory,continuous-time Markov processes.The maim contents and contributions of the dissertation are as follows:1.Based on continuous-time Markov processes,a model composed of two interact-ing complex networks is proposed to describe cooperative spreading processes wherein the virus spreading in one layer can penetrate into the other to promote the spread pro-cess.The global epidemic threshold of the model is smaller than the epidemic thresholds of the corresponding isolated networks.Thus,global epidemic onset arises in the inter-acting networks even though an epidemic onset does not arise in each isolated network.2.Considering three scenarios for different mutual influence as cooperative spread-ing,competing spreading,and the combination of the two between the two spreading processes,construct a unified model,which can unify a variety of scenarios.We get conclusions for these three scenarios.Firstly,epidemic threshold of interacting two-layer network can be risen for two competing spreading processes;secondly,epidemic threshold of interacting two-layer network can be declined for two cooperative spreading processes;thirdly,the spreading processes in layer L1 restrain the spreading processes in layer L2,and the spreading processes in layer L2 reinforce the spreading processes in L1,the epidemic threshold of L1 can be risen and that of L2 can be declined for the inter-acting networks compare with the corresponding to isolate networks.The simulations accurately verify the proof results.3.Considering the number of nodes in each layer of the multilayer coupled net-work is different,and there is a random coupling relationship between multilayer,Three models in different levels are proposed to describe cooperative spreading processes over the interconnected network,wherein the disease in one network can spread to the other.Theoretical analysis is provided for each model to reveal that the global epidemic thresh-old in the interconnected network is not larger than the epidemic thresholds for the two isolated layered networks.In particular,in an interconnected homogenous network,detailed theoretical analysis is presented,which allows quick and accurate calculations of the global epidemic threshold.Moreover,in an interconnected heterogeneous net-work with inter-layer correlation between node degrees,it is found that the inter-layer correlation coefficient has little impact on the epidemic threshold,but has significant impact on the total prevalence.