Research On The Weighted Networks For Immunization Strategies

In recent years, the research on complex networks gets more and more attention. The study of complex networks aims at commonness between different networks and finding their universal methods. Scholars have proposed different topology models to reflect the characteristics of the real social networks such as small-world networks and scale-free networks. At the same time, all sorts of infectious disease transmission models were also proposed, such as Susceptible. SI model, SIS model,SIR model, etc. According to the characteristics of different network topology models, immunization strategies are put forward. The typical immunization strategies are random immunization, targeted immunization and acquaintance immunization.Many network models (such as small-world networks and scale-free networks) tend to reflect the connectivity between nodes, and ignored how closely one node connected to other nodes. This doesn’t reflect realistic society in some cases, such as: the contact frequency of two individuals who come from same nationality is bigger than the situation from different nationality, and the contact frequency of family members is bigger than the situation between one family member and an outsider. In addition, due to the scale-free characteristics of scale-free networks, the critical value in the scale-free network is0. That means that even if the probability of the spread of the virus is small, the virus can spread in the networks continuously and stably. It also suggests that scale-free network has special fragility when it wards off infection and attacks by virus from another aspect. Therefore, in an actual social network model, an efficient and convenient immunization strategy is particularly important and urgent.Aiming at this problem, we have done the following work:(1) In order to build a model close to the actual network, we put forward a network model based on multiethnic regions and high-risk immunization strategy was used. The coefficient between regions was put forward, and we analyzed its effect in WS small-world networks and BA scale-free networks by the theory and simulation. Experiments showed that our strategy is efficient and convenient.(2) A new model on the multiethnic areas triggered that we should build another model based on interpersonal contact frequency. The relationship between nodes in the network can be described as weighted value. A bigger weighted value means that one node contact others more frequently. At the same time, high-risk immunization strategy was improved. Based on the above situation, we proposed a new method called "High-contact" immunization which only vaccinated fewer nodes and got the same or even better results. Meanwhile, we analyzed how the number of total nodes, the average of networks and the effective infection spreading rate influence the effect of immunization in networks.