[1]叶星旸.基于分数阶微分方程的木马病毒传播规律[J].集美大学学报(自然科学版),2019,24(2):145-150.
　YE Xingyang.An Epidemic Model of the Trojan Virus Propagation Based on Fractional Differential Equations[J].Journal of Jimei University,2019,24(2):145-150.
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基于分数阶微分方程的木马病毒传播规律(PDF)

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《集美大学学报（自然科学版）》[ISSN:1007-7405/CN:35-1186/N]

Title:: An Epidemic Model of the Trojan Virus Propagation Based on Fractional Differential Equations

Author(s):: YE Xingyang; (School of Science,Jimei University,Xiamen 361021,China)

Keywords:: trojan virus; fractional differential equation; equilibrium point; stability; propagation

摘要:: 建立并研究了一类基于分数阶微分方程的木马病毒传播模型，利用分数阶微分方程的相关理论，详细证明了该模型非负解的有界性、存在唯一性，分析了平衡点的存在性及其局部稳定性，并通过数值试验验证了理论结果的正确性。得到：在基本再生数小于1的情况下，未感染平衡点是局部渐近稳定的，病毒会消亡；在基本再生数大于1时，感染平衡点局部渐近稳定，病毒将扩散。根据所得到的理论结果，给出了控制木马病毒传播的有效措施。

Abstract:: In this paper,an epidemic model of trojan virus based on the fractional differential equation was studied.By means of the theory of fractional differential equations,the existence and uniqueness of the positive solution were established,then the existence and stability condition of the equilibrium of the model were analyzed.It was showed that if the basic reproduction number is less than 1,the infection free equilibrium is locally asymptotically stable,virus will die out,and if the basic reproductive number is greater than 1,the infection equilibrium is stable and the virus will spread.Some numerical experiments are carried out to confirm the obtained results.In addition,some effective measures are given to control the spread of the trojan virus.

[1]张豫川,周宗福.带有积分条件的分数阶微分方程边值问题耦合系统[J].集美大学学报(自然科学版),2013,18(4):297.
[2]陈景华,陈雪娟.Riesz空间分布阶的分数阶扩散方程的数值模拟[J].集美大学学报(自然科学版),2021,26(2):97.
　CHEN Jinghua,CHEN Xuejuan.Numerical Method for the Distributed-Order Riesz Space Fractional Diffusion Equation[J].Journal of Jimei University,2021,26(2):97.

更新日期/Last Update: 2019-05-05