基于微分方程的谣言传播模型建立与分析

Establishment and Analysis of a Rumor Propagation Model Based on Differential Equations

谣言的传播与控制已引起学术界和管理部门的高度重视.考虑谣言传播过程中官方媒体宣传对谣言易感者的影响,将谣言易感者分成两类,建立了一类新的谣言传播微分方程模型.根据Hurwitz判据、基本再生数、Lyapunov函数和LaSalle不变原理,分析模型各类平衡点的稳定性.数值试验说明了理论成果的正确性.研究结果表明,媒体宣传报道不仅能降低谣言感染率,而且还能扩大谣言易感者和传播者转化为不信谣不传谣者的数量,最终降低谣言传播对社会造成的危害.此外,适度的媒体宣传报道有助于谣言由大范围扩散向迅速消失转移趋势.

The spread and control of rumors has attracted the attention of academic and management departments.Considering the influence of official media propaganda on the susceptible persons of rumor in the process of rumor dissemination,the rumor susceptible people are divided into two categories.According to the different nature of the two types of people,a new rumor prepagation model is formulated.By using Hurwitz criterion,Lyapunov function and LaSalle invariance principle,sufficient conditions of stability are obtained and carried out by numerical simulation.Media coverage can not only reduce the rate of rumor infection,but also expand the number of rumor mongering and disseminators and reduce the harm caused by rumors to society.In addition,moderate media coverage can change the rumor from widespread to rapid disappearance.