Transmission Dynamics Analysis And Application On Complex Network

Real world,including human society and the internet,is formed by a set of components to be a complex topological structure.Based on the observations from real world networks,humans exploit mathematics tools and related knowledge to formalize a model with certain characteristics for research purpose.The formalized model is called the complex network,which is different from neither stochastic networks nor homogeneous networks.As a dynamic and hierarchical topological structure,real world networks are neither random,scale-free,nor have a single small-world.In fact,it has all the above properties.Therefore,in contrast to the random network and homogeneous network,complex network has both of their properties.With the recent advances in complex network studies,network models which are closer to real world applications are proposed,such as the heterogeneous network.In the real world,the recent massive outbreak of the virus poses a great threat to the human's lives and their properties,such as the SARS,Ebola virus,H1N1 influenza virus and so on.Therefore,it is beneficial to learn about the causes and laws of virus transmission,to formalize the transmission process,and to analyze and predict the trend according to real world observations.In the past,researchers focused on designing specific networks to study the spread of the virus,where the network models are relatively simple,and have limited characteristics of real-world networks.In this paper,a heterogeneous network is introduced.With the rule of randomness,small-world networks,random networks and scale-free networks are combined and connected to each other,producing the heterogeneous network,which is closer to complex networks in real world.On the heterogeneous network,the transmission behavior of virus transmission model with artificial immunity was studied.The contributions of this paper are as follows:First,based on the understanding of the Susceptible-Infected-Removed-Susceptible(SIRS)virus transmission model,the transmission dynamics of the SIRS virus transmission model with artificial immunity on homogeneous and inhomogeneous networks was explored.Second,according to the theory of Mean-field,the differential dynamic equation is obtained,and the corresponding propagation threshold is derived through theoretical analysis.The experimental results show that the proper adoption of artificial immunity strategy with respect to the particular network will reduce the fraction of affected nodes in the network,and effectively control the virus transmission.Third,on the heterogeneous network,the behaviors of the SIRS virus transmission model with artificial immunity was explored with and without immunization strategies.The experimental results show that the final number of affected persons is lower,in comparison with the network with a single characteristic.Therefore,due to the unique property of the heterogeneous network,it has a superior performance.