网络传播动力学.pptx

1 复杂网络传播动力学 吴 俊 国防科大信息系统与管理学院管理系 2 Spreading Dynamics on Complex Networks Disease Computer virus Rumor …… 3 SI Model （susceptible-infected） 4 SIS Model 5 SIS Model（susceptible-infected-susceptible） effective infection rate： 6 SIR Model 7 SIR Model （susceptible-infected-refractory） 疾病扩散条件： 8 Epidemic Dynamics on Complex Networks Fully Mixed  Complex Networks 9 SIS model on ER networks SIS Model on ER Networks Mean Field reaction equation for the density of infected nodes: For the steady state solution: Epidemic threshold: effective infection rate： 10 SIS model on ER networks 11 12 13 SIS model on BA networks Mean Field reaction equation for the density of infected nodes: ER BA Then for the steady state: 14 SIS model on BA networks 15 SIS model on BA networks 16 SIS model on uncorrelated SF networks 17 18 SIS model on correlated SF networks Connectivity matrix C 19 SIS model on correlated SF networks 20 21 22 SIS model on correlated SF networks 23 24 25 26 27 28 .au/simulations/networks/virus-outbreak/demo/ 29 30 Uniform Immunization In homogeneous networks, 31 Uniform Immunization In SF networks, 32 Targeted Immunization In SF networks, 33 34 Strategy I Immunize a node with probability proportional to ka, where k is the number of connections and tunes the probability of preferentially selecting high-connectivity or low-connectivity nodes. 35 Strategy II Select a node with probability proportional to ka and immunize a random acquaintance of this node. 36 Strategy III Select a random node and immunize one of its acquaintances i, with probability kia proportional to ki , where ki represents the degree of the neighbor. 37 Strategy IV 38