School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China.
College of Computer Science and Engineering, Chongqing University of Technology, Chongqing 400054, China.
Sci Rep. 2017 Feb 10;7:42308. doi: 10.1038/srep42308.
The popularity of the Web improves the growth of web threats. Formulating mathematical models for accurate prediction of malicious propagation over networks is of great importance. The aim of this paper is to understand the propagation mechanisms of web malware and the impact of human intervention on the spread of malicious hyperlinks. Considering the characteristics of web malware, a new differential epidemic model which extends the traditional SIR model by adding another delitescent compartment is proposed to address the spreading behavior of malicious links over networks. The spreading threshold of the model system is calculated, and the dynamics of the model is theoretically analyzed. Moreover, the optimal control theory is employed to study malware immunization strategies, aiming to keep the total economic loss of security investment and infection loss as low as possible. The existence and uniqueness of the results concerning the optimality system are confirmed. Finally, numerical simulations show that the spread of malware links can be controlled effectively with proper control strategy of specific parameter choice.
Web 的普及提高了网络威胁的增长。为了准确预测网络上恶意传播，制定数学模型非常重要。本文旨在了解网络恶意软件的传播机制以及人为干预对恶意超链接传播的影响。考虑到网络恶意软件的特点，通过添加另一个延迟部分，对传统的 SIR 模型进行了扩展，提出了一种新的微分传染病模型，以解决恶意链接在网络上的传播行为。计算了模型系统的传播阈值，并从理论上分析了模型的动力学。此外，还采用最优控制理论研究了恶意软件免疫策略，旨在使安全投资和感染损失的总经济损失尽可能低。确认了最优系统相关结果的存在性和唯一性。最后，数值模拟表明，通过选择适当的特定参数控制策略，可以有效控制恶意软件链接的传播。
