Mishra Bimal Kumar, Haldar Kaushik, Sinha Durgesh Nandini
Department of Mathematics, Birla Institute of Technology, Mesra, Ranchi, 835215 India.
Adjunct Assistant Professor, Department of Mathematics, Temple University, Philadelphia, USA.
Sci Rep. 2016 Jun 22;6:28289. doi: 10.1038/srep28289.
Formulating mathematical models for accurate approximation of malicious propagation in a network is a difficult process because of our inherent lack of understanding of several underlying physical processes that intrinsically characterize the broader picture. The aim of this paper is to understand the impact of available information in the control of malicious network epidemics. A 1-n-n-1 type differential epidemic model is proposed, where the differentiality allows a symptom based classification. This is the first such attempt to add such a classification into the existing epidemic framework. The model is incorporated into a five class system called the DifEpGoss architecture. Analysis reveals an epidemic threshold, based on which the long-term behavior of the system is analyzed. In this work three real network datasets with 22002, 22469 and 22607 undirected edges respectively, are used. The datasets show that classification based prevention given in the model can have a good role in containing network epidemics. Further simulation based experiments are used with a three category classification of attack and defense strengths, which allows us to consider 27 different possibilities. These experiments further corroborate the utility of the proposed model. The paper concludes with several interesting results.
由于我们对一些内在表征更广泛情况的潜在物理过程缺乏深入理解，为网络中恶意传播的精确近似制定数学模型是一个困难的过程。本文的目的是了解可用信息在控制恶意网络流行病中的影响。提出了一种1-n-n-1型微分流行病模型，其中微分性允许基于症状的分类。这是首次尝试将此类分类添加到现有的流行病框架中。该模型被纳入一个名为DifEpGoss架构的五类系统中。分析揭示了一个流行病阈值，并在此基础上分析了系统的长期行为。在这项工作中，使用了三个分别具有22002条、22469条和22607条无向边的真实网络数据集。数据集表明，模型中给出的基于分类的预防措施在控制网络流行病方面可以发挥很好的作用。进一步基于模拟的实验使用了攻击和防御强度的三类分类，这使我们能够考虑27种不同的可能性。这些实验进一步证实了所提出模型的实用性。本文以几个有趣的结果作为结论。
