Research Of Vaccination Control Strategy Based On Virus Spreading On Complex Network

Since the scale-free small-world properties and were identified, many researchesfound that lots of real networks had scale-free or small-world characteristics, complexnetworks were widely studied thoroughly. In real world, many biology networks andcommunication networks such as the Internet are typical complex network, thesenetworks are frequently suffered from virus, thus the security of complex network isextensively investigated.This paper studies how to reduce or eliminate the adverse effects of virus spreadingon the security of complex networks. There are two main methods to control thespreading of virus: first, isolate the infected nodes from the network to reduce the densityof infectious nodes, second, vaccinate some or all of the nodes to block the path oftransmission of virus. Here we devote in investigating immune to control the spreadingprocess of virus on complex network.On the basis of the fact that the vaccination ability is always restricted in real world,we presented a new nonlinear vaccination strategy, in this new strategy, the vaccinatednumber in each period was a limited small number, using theory of pulse differentialequations, we proved the existence of a "infection-free" period solution, and thesufficient global asymptotic stability condition was presented. Numeral simulationvalidated that the theory works properly. This strategy can guide immunization when thevaccination ability is restricted in real world.Consider the human subjective factor which effects vaccination in real world, wepresent another new nonlinear pulse vaccination strategy, the dynamic behavior of thespreading process of virus is analyzed, and a sufficient condition for the virus dies outwas presented. From theoretical analysis and simulation, we find that human subjectivefactor affect not only the final density of virus but also the dynamic processing. This strategy can help us understanding the vaccination process in real world, guide us tovaccinate more effectively.Finally, a summary for this thesis and some prospect in further research has beenpresented.