Weighted Network Model Of Virus Spread And Virus Immunity

In recent years, the rise of research on complex networks has made people begin to pay attention to the relationship of the network's structure complexity and the dynamics on them. The key research topics about networks include the study of topology structures and statistical characteristics in the real world and some different kinds of dynamical behaviors. Recently, the study of complex network theory is not confined to one subject but has crossed many different subjects. The findings on network research have been using to all aspects of life and promoted the development of the society. However, there are still a lot of problems unsolved. This paper mainly studies the virus spread on some complex networksSince the birth of human society, infectious diseases have been considered as head enemy by human. With the development of computer technology, computer virus has been bothering people's normal life, brings trouble also brings a great loss. Therefore, study the spreading of virus all over the world is always a focus of scientist. They study the spread features of the virus, present corresponding immunization strategies, undertake inhibition of virus to reduce the loss. Previous model is mainly to study unweighted networks, but real networks are mainly weighted networks, so study of the virus spread on weighted networks is more meaningful. This dissertation mainly studies the virus spread on three typical weighted networks, the main research results are as follows.Firstly, with using SIS model, we apply a new infection mechanism with which the probability of viral infections between two neighbors is positively correlated with their connection weight to study the dynamical behaviors of virus spread in three kinds of weighted network model which are WANG network model, BBV network model and ZHU network model. Study shows that:with the same conditions that is the network nodes, the average degrees and the average strength being same, Virus outbreak in a uniform network is faster, steady-state infection rates is higher and transient time is shorter than those in non-uniform network. The more heterogeneous the network weight distribution, the longer the transient process for virus spread, the lower the infection rate in the steady state. The ratio of initial infected nodes can affect the transient process of virus spread in the network, but it can not affect the number of infected nodes in the steady state. The smaller the probability of infected nodes recovery, the bigger the infected nodes ratio in the steady state.Secondly, with using SIR model, we apply a new infection mechanism with which the probability of viral infections between two neighbors is positively correlated with their connection weight to study the dynamical behaviors of virus spread in three kinds of weighted network model which are WANG network model, BBV network model and ZHU network model. Study shows that:The bigger the probability of removed infected nodes, the shorter the transient process of virus spread. Meanwhile, when the network reaches steady-state, the proportion of infected nodes is very low in SIR model. ZHU model and WANG model infection rates are relative bigger in steady-state, their infectious processes are also similar, BBV model infection rate is the lowest. For the not very serious infections, the removed probability is low, the transient time of virus spread in the network increases significantly.Finally, with the random immunization strategy and target immunization strategy based on the maximum weight, we study the immune effects in the three weighted networks, WANG network model, BBV network model and ZHU network model. Study shows that the maximum weight target immunization strategy is far better than random immunization strategy in the BBV network for the heterogeneity of its weight distribution. Choosing 5% nodes with heavy weights to immunize can eliminate the virus. Weight distribution is the relatively homogeneous in ZHU model and WANG model, random immunization strategy is better than the target immunization one in these networks.