Growth Of The Network And Its Spread Of Disease

As an emerging subject, the complex network has got rapid development in recent decades. In real life, complex network can be used to describe many complex systems, and in this way we can easily study the complex system. The epidemic spreading on the network is an important subject of complex network research. In the network, the nodes represent individuals and the edges represent the relationship between nodes. Thus, we can use the related methods to study the epidemic spreading among people.In reality, many networks are constantly evolving, but now most of the epidemic models are based on the static networks. In order to study the epidemic spreading on evolving networks, we consider the degree of node as a continuous variable, and proposes a modelling method based on partial differential equation. Using this method, we studies the topology structure of three different growing models. Besides, taking into account the epidemic spreading, we establish the epidemic models on growing networks. Finally, the models are simulated. The proposition of modelling method not only provides a new way for the study of topology structure, but also provides a new thinking for the epidemic modelling. More importantly, the epidemic dynamics on growing networks provides a theoretical basis for predicting and controlling the actual epidemic spreading.In chapter 1, we give an introduction to the de?nition of complex network, the research content, the research signi?cance, the characteristics and relevant theory. We also give an introduction to some important growing network models and epidemic models on networks.In chapter 2, we propose the concept of remaining degree, and establish the growing network model based on the preferential attachment of remaining degree. The degree distribution of the network model is calculated using the Mean-?eld method. Through the random simulations, it is ?nd that the network degree distribution has different forms when the ratio of the node’s maximum degree and the edge number of new nodes is different.In chapter 3, we proposes a new method which is based on partial differential equation.And, using this method, we study the topology structure of three growing networks, which are growing network with both preferential attachment and random attachment, the accelerating growing network with preferential attachment, and the BA growing network.In chapter 4, also been based on partial differential equation method, we study the epidemic spreading on networks. Firstly, we establish the continuous degree susceptibleinfected-susceptible(SIS) model on a static network. Secondly, considering the growth of networks, we establish the continuous degree SIS model on BA growing network. Finally,these models are simulated, respectively.