规则与随机网络中对逼近模型的动力学分析-应用数学专业论文.docxVIP

中北大学学位论文 中北大学学位论文 Dynamic Analysis of Pair Approximation Model In Regular and Stochastic Networks Abstract The dynamics of infectious diseases in the regular and the stochastic network is make the human individual as a space node, and make the connections between people as a figure (which may be dynamic), it is a dynamic evolution process of different node status. We consider the connection of various state nodes as the pair relationship, when we study the size change of the infective with time, it is certain to be referred to the change of pair amount of susceptible and infective to constitute. While the change of pair amount of susceptible and infective to constitute is related to the change of pair amount of susceptible and susceptible to constitute and, to the change of pair amount of infective and infective to constitute and so on. We mainly analysis the pair approximation model in the regular and stochastic networks. The first chapter, first of all the development of infectious disease dynamics model is introduced in the regular and stochastic networks, as well as the common network statistical characteristics, including the distribution of network diagram, degree and degree distribution, the pair two, pair triple, clustering coefficient, adjacency matrix, the pair approximation. And we introduction the two kinds of typical network, namely regular networks and stochastic networks; the last we introduced the relevant theoretical knowledge that need to use. The second chapter, we establish a SIS disease model of neighbor nodes satisfy Poisson distribution, then the basic reproductive number expression is obtained by using of Jacobian matrix of the disease-free equilibrium in the model, and by computing obtain the unique endemic equilibrium. Finally, the model is simulated, and verify the stability of disease-free equilibrium and the positive equilibrium point. The third chapter, firstly introduces the background of the model. Then established a pair approximatio