Research On The Predictability Of Spreading Dynamics On Complex Networks

A large range of real systems in human society could be abstracted and simplified as the complex networks, which could provide good descriptions of our familiar real-world networks, such as Internet, transportation network, science collaboration network, mo-bile communication network, online social network and so on. The studies on complex networks not only focus on the networks own statistical properties and evolution, but also pay more attention to the spreading dynamical process on networks. Based on various complex networks, predicting and analyzing the spreading dynamical process could help people to understand the real propagation problems including the disease spreading, be-havior adoption and humor diffusion, and could further provide important references for early warning and monitoring the real spreading behavior. In this thesis, we focus on studying the spreading dynamics on complex networks, pay special attention to the epi-demic threshold, prevalence and key nodes affecting the spreading process, and carry out the following researches about the predictability of spreading on complex networks:Firstly, we study the epidemic threshold from the perspective of theory and simu-lation. In view of the large fluctuation of the prevalence near the epidemic threshold, we numerically identify the SIR epidemic threshold through the variability method. The effectiveness of this numerical identification method has been verified on various net-works. Our proposed numerical method not only provides the quantitative indexes for the accuracies of the existing theoretical predictions, it is also suitable for the numerical determination of SIS epidemic threshold. Based on such numerical studies of the epi-demic threshold, we further study how the difference of recovery rates affects the SIR epidemic threshold. We propose a more general theoretical prediction framework for the SIR model with arbitrary recovery rate, and find that the obtained theoretical predictions not only agree relatively well with the numerical epidemic thresholds, but also reproduce the existing theoretical epidemic thresholds by adjusting some parameters.Then, we study the predictability of the epidemic spreading process. On the one hand, we study the epidemic variability on BA scale-free networks based on the SI spread-ing model with limited contact mode. The results show that different initial seeds hardly affect the predictability of the prevalence in the limited mode, and the predictability of the node’s infection time is affected by the special structural features of the scale-free networks at varying degree. On the other hand, based on the heterogeneous community network, we study how weak ties influence the epidemic predictability on community networks. By comparing the variability of the arrival time and prevalence of the disease for different degrees of bridge nodes, we find out that the small bridge node can enhance the epidemic predictability. Once the weak tie is given, the change of the variability of prevalence and that of the arrival time is opposite as increasing the distance between the bridge node and initial seed and the degree of the seed. Specially, the further distance and the larger degree of the initial seed can lead to the better predictability of the arrival time and the worse predictability of the prevalence. Moreover, different initial seeds will lead to different levels of the epidemic predictability as the community strength increases by varying the number of weak ties.Finally, we study the influence of different nodes in epidemic spreading. On the one hand, we study the discriminability of the node influence for fractal scale-free networks based on the flower model. By comparing the node influences of different fractal dimen-sions, we find that the discriminability of node influence remains almost unchanged with the node degree when the fractal dimension is very low. With the increase of fractal di-mension, it becomes easy to recognize the super-spreader. After introducing the network noise by randomly rewiring the links of original fractal networks, the discriminability of node influence will display an opposite trend. On the other hand, we investigate the effect of the individual response on the targeted immunization strategy aimed at hub nodes. Af-ter introducing the individual imitation mechanism into the vaccinating behavior during the disease spreading, we find that the targeted subsidy policy can be conducive to con-trolling the epidemic spreading only when the individuals prefer to imitate the strategy of individuals subsidized by the government. More importantly, increasing the proportion of subsided individuals could enlarge the final prevalence under the targeted subsidy policy. In addition, we consider the effect of the immunization strategy on the social cost. The results show that no matter how the individuals select the imitation objects, the targeted subsidy policy can always generate an optimal subsided proportion minimizing the social cost, and the proportion varies with the imitation objects.