Study Of Epidemic Spread On Complex Networks

At present, more areas on complex network are being researched, many complicated systems can be described by network. The dynamics on the network can be considered as the system dynamic properties. By studying network structure to understand and explain the system operation, thereby forecast and control network behavior. The spread of the virus in computer networks and the prevalence of infectious disease in the crowd can be viewed as a dynamic behavior on the networks. Studying the dynamics of virus can help us controlling the real virus propagation process.This thesis use complex network theory to describe the real virus propagation process. According to the real virus properties, the transmission rate which linear to the node degree was proposed and a model was created. The stability of the system was studied and the simulations validated the conclusions.In reality, the change of the node propagation speed is not linear to the change of the node degree strictly, the nonlinear transmission rate was proposed according to this feature. It means that when the node degree is relatively small, the transmission rate is linear to the degree, when the node degree is relatively large, the rate is saturated. A model was set up and some conclusions were obtained. Finally, the simulations validated these conclusions.This thesis researched vector-host virus propagation which spread by vectors. Both the vector and the host transmission rate were proposed separately, and a model which based on complex network was built. By the stability theory, some conclusions of the system were obtained and validated by simulations.