Establishment And Analysis Of SIS Dynamics Model With Correlation Coefficient On Complex Network

Complex network is an interdisciplinary subject.It is an abstract description of the actual system.The connection between the actual individual and the individual is represented by points,edges between points.With the development of network theory mature,more and more scholars are interested in the theoretical research of complex networks.Many infectious diseases in reality are actually spread through mutual contact between individuals,and they are regarded as nodes in the network.The contact between individuals is regarded as the connection between nodes in the network.Infectious disease modeling combined with complex network theory to study the transmission process of infectious disease is closer to the real transmission process than the traditional compartmental epidemic model.The correlation coefficient and clustering coefficient in the network are the basic characteristic quantities to describe the network structure.It is of profound practical significance to study the influence of network characteristic quantities on the transmission of infectious diseases.In this paper,a simple SIS infectious disease pair model was established,and the system was closed by triples approximation formula.Combined with the influence of correlation coefficient and clustering coefficient on disease transmission,the correlation coefficients between state nodes were regarded as dynamic variables,and the SIS infectious disease model with the correlation coefficients was studied.The first chapter introduces the research background of network infectious disease modeling and the current research status at home and abroad,and briefly introduces the research content and research results.In chapter 2,the influence of correlation coefficient on infectious disease modeling is considered,and the correlation coefficient between state nodes is regarded as dynamic variables.The SIS pair approximation model of infectious disease transmission under homogeneous network is established.By analyzing the stability of the disease-free equilibrium and the existence of the positive equilibrium,two different forms of equivalent infectious disease transmission thresholds were obtained.The relationship between the two thresholds was studied,and the theoretical results were verified by numerical simulation.Further,the SIS pair approximation model including birth and death is given.In Chapter 3,considering the influence of clustering coefficients on the network structure,the clustering coefficients are added to the model during the approximation process,and an SIS pair approximation model containing correlation coefficients and clustering coefficients in a static homogeneous network is established.At the same time,the existence of the disease-free equilibrium and the endemic disease equilibrium are analyzed,and the theoretical results are verified by numerical simulation.Chapter 4 summarizes this article briefly,and discusses the content that can be studied in the future.