Immunization against the Spread of Rumors in Homogenous Networks

Since most rumors are harmful, how to control the spread of such rumors is important. In this paper, we studied the process of "immunization" against rumors by modeling the process of rumor spreading and changing the termination mechanism for the spread of rumors to make the model more realistic. We derived mean-field equations to describe the dynamics of the rumor spread. By carrying out steady-state analysis, we derived the spreading threshold value that must be exceeded for the rumor to spread. We further discuss a possible strategy for immunization against rumors and obtain an immunization threshold value that represents the minimum level required to stop the rumor from spreading. Numerical simulations revealed that the average degree of the network and parameters of transformation probability significantly influence the spread of rumors. More importantly, the simulations revealed that immunizing a higher proportion of individuals is not necessarily better because of the waste of resources and the generation of unnecessary information. So the optimal immunization rate should be the immunization threshold.由于多数谣言均具有危害性，管控此类谣言的传播具有重要意义。本文通过构建谣言传播模型，并修改谣言传播的终止机制以提升模型的现实合理性，对谣言的“免疫”过程展开研究。我们推导了用于描述谣言传播动力学的平均场方程（mean-field equations）。通过开展稳态分析，我们得到了谣言实现传播所需突破的传播阈值。此外，我们进一步探讨了可行的谣言免疫策略，并推导出用于表征阻止谣言传播所需最低水平的免疫阈值。数值模拟结果表明，网络平均度与转换概率参数对谣言传播具有显著影响。更为关键的是，模拟结果显示，由于资源浪费与冗余信息的产生，提高个体免疫比例未必能带来更好的效果，因此最优免疫率应等于免疫阈值。