Immunization strategies on complex networks are effective methods to control the spreading dynamics on complex networks, which change the topology and connectivity of the underlying network, thereby affecting the dynamics process of propagation. Here, we use a non-Markovian threshold model to study the impact of immunization strategies on social contagions, in which the immune index greater than (or equal to) 0 corresponds to targeted (random) immunization, and when the immune index is less than 0, the probability of an individual being immunized is inversely related to the degree of the individual. A generalized edge-based compartmental theory is developed to analyze the dynamics of social contagions under immunization, and theoretical predictions are very consistent with simulation results. We find that increasing the immune index or increasing the immune ratio will reduce the final adoption size and increase the outbreak threshold, in other words, make the residual network after immunization not conducive to social contagions. Interestingly, enhancing the network heterogeneity is proved to help improve the immune efficiency of targeted immunization. Besides, the dependence of the outbreak threshold on the network heterogeneity is correlated with the immune ratio and immune index.

中文翻译：

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免疫策略对社会传染动态的影响

复杂网络上的免疫策略是控制复杂网络上传播动态的有效方法，可改变底层网络的拓扑和连接性，从而影响传播的动态过程。在这里，我们使用非马尔可夫阈值模型来研究免疫策略对社会传染的影响，其中免疫指数大于（或等于0）对应于有针对性的（随机）免疫，而免疫指数小于0，个体被免疫的可能性与个体的程度成反比。建立了基于边缘的广义区室理论来分析免疫接种过程中社会传染的动态，理论预测与模拟结果非常吻合。我们发现增加免疫指数或增加免疫比率将减少最终采用的规模并增加爆发阈值，换句话说，使免疫后的残留网络不利于社会传染。有趣的是，事实证明，增强网络异质性有助于提高靶向免疫的免疫效率。此外，爆发阈值对网络异质性的依赖性与免疫率和免疫指数相关。