Dynamic Analysis Of Pair Approximation Model In Regular And Stochastic Networks

The dynamics of infectious diseases in the regular and the stochastic network is make thehuman 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. Weconsider the connection of various state nodes as the pair relationship, when we study the sizechange of the infective with time, it is certain to be referred to the change of pair amount ofsusceptible and infective to constitute. While the change of pair amount of susceptible andinfective to constitute is related to the change of pair amount of susceptible and susceptible toconstitute 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 isintroduced in the regular and stochastic networks, as well as the common network statisticalcharacteristics, including the distribution of network diagram, degree and degree distribution,the pair two, pair triple, clustering coefficient, adjacency matrix, the pair approximation. Andwe introduction the two kinds of typical network, namely regular networks and stochasticnetworks; 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 Poissondistribution, then the basic reproductive number expression is obtained by using of Jacobianmatrix of the disease-free equilibrium in the model, and by computing obtain the uniqueendemic equilibrium. Finally, the model is simulated, and verify the stability of disease-freeequilibrium and the positive equilibrium point.The third chapter, firstly introduces the background of the model. Then established apair approximation disease dynamics model of two strains of independent existence, theexpression of the basic reproductive number of the model, and the existence conditions of boundary equilibrium and positive equilibrium are obtained by dynamic analysis. Finally wevalidated the stability of disease-free equilibrium, boundary equilibrium and the endemicequilibrium by using numerical simulation method.