基于分数阶微分方程的手机病毒传播模型研究.pdf

Advances in Applied Mathematics 应用数学进展, 2017, 6(9), 1229-1235 Published Online December 2017 in Hans. /journal/aam /10.12677/aam.2017.69148 An Epidemic Model Research of the Mobile Phone Virus Based on Fractional Differential Equations Xingyang Ye School of Science, Jimei University, Xiamen Fujian th nd th Received: Dec. 5 , 2017; accepted: Dec. 22 , 2017; published: Dec. 29 , 2017 Abstract With the increasing popularity of mobile phones, the spread of mobile virus has become increa- singly serious. Therefore, the study of the spread of the virus is necessary. In this paper, we first establish an epidemic model of mobile phone virus based on the fractional differential equation. Then by means of the theory of fractional differential equations, we analyse the existence and sta- bility condition of the equilibrium of the model. It is showed that if the basic reproduction number is less than 1, the infection free equilibrium is locally asymptotically stable and 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 mobile virus, which pro- vides referential support for virus prediction, control and prevention. Keywords Mobile Virus, Fractional Differential Equation, Equilibrium Point, Stability 基于分数阶微分方程的手机病毒传播模型研究 叶星旸 集美大学理学院，福建 厦门 收稿日期：2017年12月5 日；录用日期：2017年12月22 日；发布日期：2017年12月29 日 摘 要 随着手机普及率的提高，手机病毒的传播也愈发严重。因此，对于病毒传播规律的研究必不可少。本文 文章引用: 叶星旸. 基于分数阶微分方程的手机病毒传播模型研究[J]. 应用数学进展, 2017, 6(9): 1229-1235. DOI: 10.12677/aam.2017.69148 叶星旸