Research Of Transmission Dynamics Of Infectious Diseases On Weak Clustered Networks

The networks formed by individual contacts have an obvious clustering feature,which means my friend’s friend may be a friend of mine.This type of networks have an important effect on the spread of diseases.This paper study the effects of the clique’s size and the clique’s numbers on the spread of diseases,the model more reasonable for the individual contact.Firstly,Chapter 1 introduces the research significance and the research background,then introduces our research contents of this paper.In Chapter 2,by making use of percolation theory and the method of tree structure to analyze the spread of disease on the weak clustered networks.By establishing the multidimensional joint distribution function,we can calculate the percolation threshold of the giant connected component(GCC)and the expected fractional size of the GCC.In the condition of the random network with poisson distribution,study the effects of the clique’s size and the clique’s numbers on the spread of diseases by the numerical and stochastic simulation.In Chapter 3,considers a class of clustered networks which contains arbitrary 3-cliques and4-cliques,and establishes the multidimensional joint distribution function.By using the generating function to calculate the probability that one node belongs to the GCC,the expected size of the connected component that one node is connected and the percolation threshold of the GCC.At the same time,applys the bond percolation process to the spread of SI epidemic model.We study the effects of the global clustering coefficient on the existence of the GCC by numerical simulations.The above results have a great significance for deeply understanding the influence of the clustering coefficient on the disease’s outbreak.In Chapter 4,Summarize the main conclusion of this paper and investigate some ideas for future research.