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Modeling and analyzing the dynamic spreading of epidemic malware by a network eigenvalue method

机译：利用网络特征值方法对流行性恶意软件的动态传播进行建模和分析

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This paper mainly focuses on studying the influence of network characteristics on malware spreading. Firstly, a generalized model with weakly-protected and strongly-protected susceptible nodes is developed by considering the possibility of an intruded node converting back to a weakly-protected susceptible one. The dynamics of the generalized compartmental model is intensively discussed and analyzed, deriving several sufficient conditions for its global stability. Following this work, a novel node-based model is newly proposed to describe malware propagation over an arbitrary connected network including synthesized and real networks. From a microscopic perspective, we establish the novel model by introducing several different variables for each node which describe the probabilities of a node locating at respective states. Our theoretical analysis shows that the largest eigenvalue of the propagating network is a key factor determining malware prevalence. Specifically, the range of the leading eigenvalue can be split into three subintervals in which malware approaches extinction very quickly, or tends to extinction, or persists, depending on into which subinterval the largest eigenvalue of the propagating network falls. Theoretically, the trivial equilibrium of our new node-based model is clearly proved to be exponentially globally stable when the maximum eigenvalue is less than a threshold. We also illustrate the predictive effectiveness of our model by designing some numerical simulations on some regular and scale-free networks. Consequently, we conclude that malware prevalence can be effectively prevented by properly adjusting the spreading network, e.g., reducing the number of nodes and deleting some edges, so that its maximum eigenvalue falls into the appropriate subinterval. (C) 2018 Elsevier Inc. All rights reserved.
机译：本文主要研究网络特征对恶意软件传播的影响。首先，通过考虑入侵节点转换回弱保护易感节点的可能性，建立了具有弱保护和强保护易感节点的通用模型。深入讨论和分析了广义隔室模型的动力学，从而得出了其整体稳定性的若干充分条件。继这项工作之后，新提出了一种新颖的基于节点的模型来描述恶意软件在包括合成网络和真实网络在内的任意连接网络上的传播。从微观的角度来看，我们通过为每个节点引入几个不同的变量来建立新颖的模型，这些变量描述了节点处于各自状态的概率。我们的理论分析表明，传播网络的最大特征值是决定恶意软件流行程度的关键因素。具体而言，前导特征值的范围可以分为三个子间隔，在这些子间隔中，恶意软件会迅速消失，趋于灭绝或持续存在，这取决于传播网络的最大特征值落入哪个子间隔。从理论上讲，当最大特征值小于阈值时，新的基于节点的模型的平凡平衡被证明是全局指数稳定的。我们还通过在一些常规且无标度的网络上设计一些数值模拟来说明模型的预测有效性。因此，我们得出结论，可以通过适当地调整传播网络来有效地防止恶意软件流行，例如，减少节点数量并删除一些边缘，以使其最大特征值落入适当的子间隔。 （C）2018 Elsevier Inc.保留所有权利。

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