Establishment And Analysis Of SIR Epidemic Model With Correlation Coefficients

Human health and social development are closely related to infectious diseases.Therefore,it is of great significance to study transmission mechanism with aim of taking effective measures to control the epidemic.Infectious disease dynamics are using mathematical models to study the spread of diseases.Because community diseases are spread mainly through social contact networks,using the complex network theory to formulate models could refine relevant mechanisms,which is more in line with reality.In the past few decades,the moment closed methods of network epidemic model have been extensively studied.It is quite significant to study how the characteristics of network affect epidemic.Therefore,the correlation coefficients are regarded as dynamic variables and using the pair approximation method to close the model,and research is carried out in static homogeneous networks,dynamic homogeneous networks and heterogeneous networks,respectively.In chapter 1,the topological structure of networks and the significance of network epidemic modeling are introduced.Additionally,research of moment closed methods and the characteristics of networks in infectious disease modeling are depicted.Finally,it gives the research contents and methods of this paper.In chapter 2,we develop a SIR epidemic dynamic model with correlation coefficients in static networks.The existence of disease-free equilibrium is analyzed,and various conditions of diseasefree equilibrium are given.The main results of this chapter are verified by numerical simulation.In chapter 3,in the case of birth and death,we establish a SIR epidemic dynamic model with correlation coefficients,and the stability of disease-free equilibrium and the existence of endemic equilibrium are used respectively.Two different thresholds are obtained.Especially when the clustering coefficient is zero,the relationship between two thresholds is given.Finally,the main results of this chapter are verified by numerical simulation.In chapter 4,considering the degree distribution of the network,a SIR epidemic dynamic model with correlation coefficients is established by using the method of probabilistic generating function in heterogeneous networks,and the existence of disease-free equilibrium is analyzed.In Chapter 5,Summarize the main conclusion of this paper and do some expectation for future.