Structure Identification Of Network In Disease Transmission

The topology of a complex network plays an important role in the evolution mech-anism and behavior function of the network,and can promote to control the dynamic mechanism of the network well.For example,if we make the topology of some dis-ease spreading network clear,the relevant departments can more effectively inhibit the outbreak and propagation of infectious diseases.However,in real life,the topology of a network is often unknown,and only a large number of node dynamics that may contain noise can be observed.Therefore,it is of great significance to design some mathematical methods to dig and deduce the topology of complex network from these data.The main work of this paper is as follows:The first chapter introduces the preliminaries,including some basic definitions in complex networks,several classical network models,and several classical disease transmission models.In the second chapter,we introduce the models and related algorithms of the optimization problem related to compressive sensing,including the optimality condition,sparse optimization,SLO algorithm for solving the minimization of norms of l0,ADMM algorithm.In the third chapter,firstly,considering that the exchange of information and node behavior is to promote or restrict each other in a real social network,we establish a more realistic model of disease transmission.Through this model,we simulate the outbreak of a disease in that social network and observe the state information of the nodesSecondly,on the one hand,we use strict mathematical theory to prove and deduce the rationality of the transformation between the problem of topology identification in disease transmission model and a sparse optimization problem.On the other hand,in order to verify the effect of recognition by using AD MM algorithm,we use ER random network model and WS small world network model for numerical simulation,the results show that the method is good to identify.Thirdly,in fact,the data we observe can not be 100 percent accurate,so we add noise interference to the experimental data.We use the same method for the ER random network model and the WS small world network model.The numerical simulations show that our method is robust.Finally,all the content is summarized and future work is prospected.