Research On Virus Spreading Model And Control Strategy In Adaptive Networks

Complex network is a kind of intersecting research that refers to muti-fields and muti-subjects. More and more problems which are according to nonlinear science, information science, sociology, biology, economics etc are reflected and described by the viewpoint of network. Different math models are proposed to describe different networks with different characteristic. Meanwhile, many typical epidemic propagation models have been proposed to study the virus propagation that including dynamics characteristic and control strategy on the network. And based on this two aspects, the main content is as follows.Firstly, the basic theory of complex network is reviewd, as basic concepts, typical network models and virus propagation models are briefly introduced. And also the latest research status and significant trends of adaptive networks are concluded and analyzed from two aspects, research methods and controlling strategy.And then based on a specific adaptive epidemic spreading model, in which the resetting probability is affected significantly, linearly and positively by the virus transmission rate, a modified Susceptible-Infected-susceptible epidemic model with varied resetting probability in adaptive networks is presented. Epidemic spreading dynamics is studied by nonlinear differential dynamic system. The existing condition and local stability of the equilibrium in this network model are investigated by analyzing its corresponding characteristic equation of Jacobian Matrix of the nonlinear system. It is shown that when the epidemic threshold0 R ?1, the disease-free equilibrium is asymptotically locally stable and endemic equilibrium does not exist. And if0 R ?1, the disease-free equilibrium is not stable and there exist the only asymptotically locally stable endemic equilibrium. Numerical simulations are given to verify the results of theoretical analysis. The result shows that when the epidemic threshold is less than 1, the disease will die out; and when the epidemic threshold is greater than 1, the disease will continue to spread in the network.Finally, an immunization strategy that based on local reliability is presented, which uses the node’s local reliability as the immunization priority. For the strategy do not have to obtain the whole situation of the network, just as the acquaintance immunization, its feasibility is guaranteed. Comparing with targeted immunization and acquaintance immunization, numerical simulations are given to research and analyze the epidemic threshold and immunization effects. And results show that local reliability immunization is better than acquaintance immunization and a bit worse than targeted immunization.