{"title":"A SEIQRS Computer Virus Propagation Model and Impulse Control With Two Delays","authors":"JunLing Wang, Xinxin Chang, Lei Zhong","doi":"10.1002/mma.10721","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>Computer viruses have caused great harm and nasty effects on people's lives. Therefore, analyzing and establishing the corresponding mathematical model can help explore and study the propagation law of computer viruses. On this basis, we apply the theory of computer virus propagation dynamics by combining computer viruses and the variability of their removal rates of different states in the network. The study presents a new Susceptible-Exposed-Infected-Quarantine-Recovered-Susceptible (SEIQRS) computer virus propagation model with two delays. In addition, we introduce impulse control, an optimal control method, to explore the effect of the impulse period on the model. We first derive the basic reproduction number of the model. Then, the characteristic equations and eigenvalues are discussed analytically by controlling the delay parameters variation in order to analyze local stability and Hopf bifurcation for the computer virus model. Next, we add impulse control and find that it could better control the propagation of computer viruses. Firstly, we analyze the dynamical behavior of this model using the relevant theories of time delay differential equations to provide a theoretical basis for the effective elimination and control of virus propagation in computer networks. Secondly, we use Matlab to conduct numerical simulations, which verify the correctness of theoretical results. Finally, we synthesize the theoretical and experimental analysis of the present model to provide some scientific suggestions for better control of the spreading of computer viruses.</p>\n </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6851-6865"},"PeriodicalIF":2.1000,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.10721","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Computer viruses have caused great harm and nasty effects on people's lives. Therefore, analyzing and establishing the corresponding mathematical model can help explore and study the propagation law of computer viruses. On this basis, we apply the theory of computer virus propagation dynamics by combining computer viruses and the variability of their removal rates of different states in the network. The study presents a new Susceptible-Exposed-Infected-Quarantine-Recovered-Susceptible (SEIQRS) computer virus propagation model with two delays. In addition, we introduce impulse control, an optimal control method, to explore the effect of the impulse period on the model. We first derive the basic reproduction number of the model. Then, the characteristic equations and eigenvalues are discussed analytically by controlling the delay parameters variation in order to analyze local stability and Hopf bifurcation for the computer virus model. Next, we add impulse control and find that it could better control the propagation of computer viruses. Firstly, we analyze the dynamical behavior of this model using the relevant theories of time delay differential equations to provide a theoretical basis for the effective elimination and control of virus propagation in computer networks. Secondly, we use Matlab to conduct numerical simulations, which verify the correctness of theoretical results. Finally, we synthesize the theoretical and experimental analysis of the present model to provide some scientific suggestions for better control of the spreading of computer viruses.
期刊介绍：
Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome.
Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted.
Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.
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