关键词: 谣言传播, SIR模型, 平均场方程, 稳定状态, 感染峰值

Abstract: To solve the problem that infected nodes move out of the system during the process of rumor propagation, a new SIR (Susceptible-Infective-Removal) rumor propagation model on dynamic homogeneity network was proposed by improving the normalization conditions of classical SIR rumor propagation model. Firstly, according to the propagation rules and mean field theory, the rumor propagation dynamics equation was established on the homogenous network. Then the steady state and infection peak of the rumor propagation process were theoretically analyzed. Finally, the influence of factors on rumor propagation was studied through numerical simulation, which including infection rate, immune rate, real immune coefficient and average degree of network. Research indicates that, as infected nodes move out of the system, steady state value decreases and infection peak slightly increases, compared with the classical SIR rumor propagation model. The study also shows that the peak value of rumor infection increases as the infection probability increases and the immune probability decreases. As the real immune coefficient increases, the steady state value of immune nodes increases. The network average degree has no influence on the steady state of rumor propagation. The larger the average degree is, the earlier the arrival time of the infection peak. This research expands the application scope of SIR propagation model from a closed system to a non-closed system, providing guidance theory and numerical support for making rumor prevention measures.

Key words: rumor propagation, SIR (Susceptible-Infective-Removal) model, mean field equation, steady state, infection peak