The mobile networks have increasingly facilitated our daily life but are also breeding grounds for malicious worms, which are considered as the main threat to cyber security. The purpose of this paper is to analyze the dynamics of worm propagation and to control the worm epidemic based on mobile-phone networks. Accordingly, we establish an SEIQR-type model to explore the worm epidemic with saturated incidence rate. This paper shows that if the basic reproduction number is less than 1, the worm-free equilibrium is asymptotically stable, and the epidemic of worm will eventually disappear and remain under control; in addition, if the basic reproduction number is greater than 1, the asymptotical stability of worm-existence equilibrium is derived to imply that the epidemic will remain persistent and uncontrollable. Our results give new insights to mobile network security, namely, that is predicting the worm spreading tendency, identifying the epidemic control strategies, and estimating the worm popularity level. Numerical experiments are conducted to show the rationality of our obtained results and the effectiveness of the control strategies.

中文翻译：

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基于SEIQR型饱和发病率模型的移动网络蠕虫流行病学动态与控制

移动网络日益便利了我们的日常生活，但同时也成为了恶意蠕虫的温床，这些蠕虫被认为是对网络安全的主要威胁。本文的目的是分析蠕虫传播的动力学并控制基于手机网络的蠕虫流行。因此，我们建立了一个SEIQR型模型来探索具有饱和发生率的蠕虫流行。本文表明，如果基本繁殖数小于1，则无蠕虫的平衡是渐近稳定的，蠕虫的流行最终将消失并受到控制。另外，如果基本繁殖数大于1，则表明蠕虫存在平衡的渐近稳定性表示该流行病将持续存在并且无法控制。我们的结果为移动网络安全提供了新的见解，即预测蠕虫的传播趋势，确定流行控制策略并估计蠕虫的流行程度。进行了数值实验，以证明我们获得的结果的合理性和控制策略的有效性。