官方媒体影响下的随机谣言传播模型
Stochastic Rumor Propagation Model under the Influence of Official Media
摘要:
在添加官方媒体对谣言传播易感染者影响下的确定性方程中，考虑影响因子γ受环境噪声的扰动，建立官方媒体影响下的随机微分方程，并研究了在无谣言平衡点和正平衡点附近的渐近性质。证明了该随机微分方程的正解存在唯一性。然后，定义了新的基本再生数ℜ
'0，并证明了满足一定条件时，系统的解在无谣言平衡点附近是渐近稳定的；而当满足另外四点要求时，系统的解在正谣言平衡点附近是渐近稳定的。
Abstract:
In addition to the deterministic equation under the influence of the official media on the rumor propagation of susceptible infected people, the stochastic differential equation under the influence of the official media is established by considering the disturbance of the influence factor by environmental noise, and the asymptotic properties near the rumor free equilibrium point and positive equilibrium point are studied. First, the existence and uniqueness of positive solutions of the stochastic differential equation are proved. Then, a new basic reproduction number ℜ'0 is defined. And it is proved that when certain conditions are satisfied, the solution of the system is asymptotically stable near the rumor free equilibrium point. When the other four requirements are met, the solution of the system is asymptotically stable near the positive rumor equilibrium point.
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