The Research Of The Improved SIR Model Based On Complex Networks

In the real world,many complex systems can be abstracted as complex networks to analyze and research. The universal method is to extract the main features of the studied network and build the corresponding network model. Combined with the interdiscipline, the rules of network evolutionary process as well the relationship between the structure and the function of complex network and are studied. The multiple forms of communication phenomenon on the complex network can be regarded as the propagation behavior that follows approximately a certain rule. The actual complex network system has many elements and complicated organization structure, which makes the propagation laws of information on the network complicated. As a result, there is urgent to construct the reasonable complex network model and the information dissemination model to explain the law of the network communication and solve relevant problems. This dissertation mainly focuses on the research of epidemic disease spreading model on the complex network and the rumor spreading model on the social network.The contents are as follows:Firstly, several basic static statistical characteristics parameters of the complex network are introduced. Some kinds of classic network models and their characteristic parameters are also described in detail. Moreover, different models of disease transmission and rumor spreading on the complex network are compared in this dissertation.Secondly, for the deficiency of the epidemic propagation models lacking of multiple infections stages, referring to the characteristics of two traditional propagation models including SIR and SEIR, an improved SIR epidemic propagation model with multi-infectious stages,named SInR model),was put forward. Different infectious stages with non-uniform infectiousness which impacts on the spread of the epidemic in different network structures and the spread threshold were considered; meanwhile, relative infectiousness and propagation time were introduced to the model, and the simulations on network construction, network scale and relative infectiousness were also given. The simulation results show that epidemic disease spreads faster and the influence range is larger on scale-free network under this model. In addition, the spread threshold value of relative infectiousness of scale-free network is less than the small world’s and setting a reasonable threshold is beneficial to reduce the influence of the propagation of epidemic disease.Thirdly, for the problem that rumors spreading on social network more and more serious, this paper proposed a new CASR(Credulous-Affected-Spreader-Rationals) rumor spreading model based on the SIR model,while considering the rumor acceptant probability function. For the rumor acceptant probability function, positive and negative media effect, rumor receiving reinforced signal effect and trust value factors were considered. With the variances of parameters, the simulation on the small world network with local scale free structure results show that under the positive effect, the media factor and trust value can reduce the probability of an individual to accept rumor, which restrains the spreading of the rumor; conversely, under the positive effect, the media factor and trust value can increase the probability of an individual to accept rumor, which is beneficial to the rumor propagation.