SONG Li-peng, ZHANG Rong-ping
（School of Computer and Control Engineering, North University of China, Taiyuan 030051, China）
Abstract： The threat of malware in wireless sensor network has stimulated some activities to model and analyze the malware prevalence. To understand the dynamics of malware propagation in wireless sensor network, we propose a novel epidemic model named as e-SEIR (susceptible-exposed-infectious-recovered) model, which is a set of delayed differential equations, in this paper. The model has taken into account the following two factors: ① Multi-state antivirus measures; ② Temporary immune period. Then, the stability and Hopf bifurcation at the equilibria of linearized model are carefully analyzed by considering the distribution of eigenvalues of characteristic equations. Both mathematical analysis and numerical simulations show that the dynamical features of the proposed model rely on the basic reproduction number R0 and time delay τ. This novel model can help us to better understand and predict the propagation behaviors of malware in wireless sensor networks.
Key words： wireless sensor network； stability； Hopf bifurcation； epidemic model； time delay
CLD number： TP309.5Document code： A
Article ID： 1674-8042（2016）02-0136-09 doi： 10.3969/j.issn.1674-8042.2016.02.007
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无线传感网络病毒传播模型的动力学分析
宋礼鹏， 张蓉萍
（中北大学 计算机与控制工程学院， 山西 太原 030051）
摘要:由于无线传感网络病毒具有的危害性， 存在一些针对该类病毒建模与分析的研究活动。 为了进一步研究无线传感网络病毒的传播特性， 本文提出一个新病毒模型， 即e-SEIR模型。 该模型由一系列时滞微分方程组成。 模型中考虑了两方面的因素： ① 多阶段的反病毒措施； ② 免疫的时效性。 通过给出线性化模型对应特征方程的特征根分布， 文中分析了模型平衡态的稳定性和Hopf分支。 进一步对模型进行了理论分析和数值仿真， 结果均表明模型的动力学特性依赖于基本再生数 R0 和时滞参数 τ。 本文给出的模型有助于更好地理解和预测无线传感网络病毒的传播行为。
关键词:无线传感网络； 稳定性； Hopf分支； 流行病模型； 时滞
引用格式：SONG Li-peng, ZHANG Rong-ping. Dynamical analysis for a malware propagation model in wireless sensor network. Journal of Measurement Science and Instrumentation, 2016, 7(2)： 136-144. ［doi： 10.3969／j.issn.1674-8042.2016.02.007］
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